7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 3\",\"description\":\"Lines, angles, and triangles fundamentals.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-lines-angles-triangles-quiz-3\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Geometry and Trigonometry - Lines, angles, and triangles\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 3\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-lines-angles-triangles-quiz-3\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 3"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Lines, angles, and triangles fundamentals.

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$undefined",["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M8.228 9c.549-1.165 2.03-2 3.772-2 2.21 0 4 1.343 4 3 0 1.4-1.278 2.575-3.006 2.907-.542.104-.994.54-.994 1.093m0 3h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Questions"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":10}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Level"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced"}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Category"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Geometry and Trigonometry - Lines, angles, and triangles"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2488,"prismaId":"cmpz9rmb00fthjglljjfn8ppy","slug":"psat-8-9-lines-angles-triangles-quiz-3","title":{"rendered":"Quiz 3"},"content":{"rendered":"

Practice problems on lines, angles, and triangles for PSAT 8/9.

"},"excerpt":{"rendered":"

Lines, angles, and triangles fundamentals.

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Geometry and Trigonometry - Lines, angles, and triangles","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8f0zo0yk4jg8wd4qzxl8x","texte_question":"$18","type_question":"QCM","explication":"

A dilation changes side lengths but does not change angle measures.

Triangle $$ABC$$ is dilated to obtain triangle $$XYZ$$.

So, corresponding angles are congruent.

Angle $$A$$ corresponds to angle $$X$$.

The measure of angle $$A$$ is $$60^\\circ$$.

Therefore, the measure of angle $$X$$ is also $$60^\\circ$$.

Final answer: $$60^\\circ$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$20$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$57$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$63$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0zt0ykajg8wcq7it46f","texte_question":"$19","type_question":"QCM","explication":"

The angle marked $$110^\\circ$$ is an exterior angle at $$C$$.

The interior angle $$\\angle BCA$$ and the exterior angle form a linear pair.

$$\\angle BCA+110=180$$

Subtract $$110$$ from both sides.

$$\\angle BCA=70$$

The problem states that $$\\angle BAC$$ is equal to $$\\angle BCA$$.

So:

$$\\angle BAC=70$$

Use the triangle angle sum.

$$70+70+x=180$$

$$140+x=180$$

$$x=40$$

Final answer: $$40$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$110$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$70$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$55$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$40$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f1030ykgjg8w7123lgaz","texte_question":"$1a","type_question":"QCM","explication":"

The triangles are similar. Similar triangles have congruent corresponding angles.

Triangle $$CAE$$ is similar to triangle $$CBD$$.

So, angle $$CAE$$ corresponds to angle $$CBD$$. The measure of angle $$CBD$$ is $$57^\\circ$$. Therefore, the measure of angle $$CAE$$ is also $$57^\\circ$$.

Final answer: $$57^\\circ$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$(26\\cdot57)^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(26+57)^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$57^\\circ$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$26^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10a0ykmjg8wvbtalq5l","texte_question":"

In triangle $$ABC$$, angle $$B$$ is a right angle. Point $$D$$ lies on $$AC$$, and point $$E$$ lies on $$AB$$ such that $$DE$$ is parallel to $$BC$$. If the measure of angle $$ABC$$ is $$90^\\circ$$ and the measure of angle $$ACB$$ is $$28^\\circ$$, what is the measure, in degrees, of angle $$AED$$?

","type_question":"TexteLibre","explication":"

Since $$DE$$ is parallel to $$BC$$, angle $$AED$$ corresponds to angle $$ABC$$.

Corresponding angles formed by parallel lines are congruent.

The measure of angle $$ABC$$ is $$90^\\circ$$.

Therefore, the measure of angle $$AED$$ is also $$90^\\circ$$.

Final answer: $$90$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10e0ykpjg8wjkhc4oed","texte_question":"

Quadrilaterals $$LMNO$$ and $$PQRS$$ are similar, where $$L$$, $$M$$, and $$N$$ correspond to $$P$$, $$Q$$, and $$R$$, respectively. The measure of $$\\angle O$$ is $$120^\\circ$$. What is the measure of $$\\angle S$$?

","type_question":"QCM","explication":"

Similar figures have congruent corresponding angles.

The order of the letters shows the corresponding vertices.

$$L$$ corresponds to $$P$$.

$$M$$ corresponds to $$Q$$.

$$N$$ corresponds to $$R$$.

Therefore, $$O$$ corresponds to $$S$$.

The measure of angle $$O$$ is $$120^\\circ$$.

So, the measure of angle $$S$$ is also $$120^\\circ$$.

Final answer: $$120^\\circ$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$30^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$120^\\circ$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$240^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10h0ykvjg8wfoqsr2rj","texte_question":"

In triangle $$XYZ$$, the measure of angle $$X$$ is $$40^\\circ$$. If triangle $$XYZ$$ is isosceles, which of the following is NOT a possible measure of angle $$Y$$?

","type_question":"QCM","explication":"

In an isosceles triangle, two angles must be equal. Angle $$X$$ is $$40^\\circ$$.

One possible case is:

$$Y=40^\\circ$$

Another possible case is that the two equal angles are not angle $$X$$.

Then: $$Y=Z$$

Use the triangle angle sum.

$$40+Y+Y=180$$

$$40+2Y=180$$

$$2Y=140$$

$$Y=70$$

So, possible values of angle $$Y$$ include $$40^\\circ$$ and $$70^\\circ$$.

The value $$50^\\circ$$ is not possible.

Final answer: $$50^\\circ$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$40^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$50^\\circ$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$70^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$100^\\circ$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10k0yl1jg8wefgkitci","texte_question":"

In right triangle $$DEF$$, angle $$F$$ is the right angle and $$EF=120$$. Point $$G$$ lies on side $$DF$$, and point $$H$$ lies on side $$DE$$ such that $$GH$$ is parallel to $$EF$$ and $$DG=3GF$$. What is the length of line segment $$GH$$?

","type_question":"TexteLibre","explication":"

Since $$GH$$ is parallel to $$EF$$, triangle $$DGH$$ is similar to triangle $$DFE$$.

The segment $$DF$$ is split so that:

$$DG=3GF$$

So, the full length $$DF$$ is:

$$DF=DG+GF$$

Since $$DG=3GF$$:

$$DF=3GF+GF=4GF$$

Therefore:

$$\\frac{DG}{DF}=\\frac{3GF}{4GF}=\\frac{3}{4}$$

Because the triangles are similar:

$$\\frac{GH}{EF}=\\frac{DG}{DF}$$

Substitute $$EF=120$$.

$$\\frac{GH}{120}=\\frac{3}{4}$$

Multiply.

$$GH=120\\cdot\\frac{3}{4}$$

$$GH=90$$

Final answer: $$90$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10m0yl4jg8w0nnqldld","texte_question":"

Triangle $$PQR$$ is similar to triangle $$XYZ$$, where $$P$$, $$Q$$, and $$R$$ correspond to $$X$$, $$Y$$, and $$Z$$, respectively. In triangle $$PQR$$, the length of $$PQ$$ is $$90$$ and the length of $$QR$$ is $$180$$. In triangle $$XYZ$$, the length of $$YZ$$ is $$30$$. What is the length of $$XY$$?

","type_question":"QCM","explication":"

The triangles are similar. The corresponding sides are:

$$PQ \\leftrightarrow XY$$ $$QR \\leftrightarrow YZ$$

Use the scale factor from triangle $$PQR$$ to triangle $$XYZ$$.

$$\\frac{YZ}{QR}=\\frac{30}{180}$$

Simplify.

$$\\frac{30}{180}=\\frac{1}{6}$$

Apply the same scale factor to $$PQ$$.

$$XY=90\\cdot\\frac{1}{6}$$

$$XY=15$$

Final answer: $$15$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$15$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$30$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$45$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10p0ylajg8w3k8f1jol","texte_question":"

A line intersects two parallel lines, forming acute and obtuse angles. The measure of one acute angle is $$(5x+20)^\\circ$$, and the adjacent obtuse angle is $$(12x-10)^\\circ$$. What is the value of $$x$$?

","type_question":"TexteLibre","explication":"

An acute angle and its adjacent obtuse angle form a linear pair. A linear pair has a sum of $$180^\\circ$$. Set up the equation.

$$(5x+20)+(12x-10)=180$$

Combine like terms.

$$17x+10=180$$

Subtract $$10$$ from both sides.

$$17x=170$$

Divide both sides by $$17$$.

$$x=10$$

Final answer: $$10$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f10s0yldjg8wfddoi7y5","texte_question":"

In triangle $$DEF$$, the measure of angle $$D$$ is $$62^\\circ$$, the measure of angle $$E$$ is $$90^\\circ$$, and the measure of angle $$F$$ is $$\\left(\\frac{m}{2}\\right)^\\circ$$. What is the value of $$m$$?

","type_question":"QCM","explication":"

The sum of the interior angles of a triangle is $$180^\\circ$$.

Set up the equation.

$$62+90+\\frac{m}{2}=180$$

Add the known angles.

$$152+\\frac{m}{2}=180$$

Subtract $$152$$ from both sides.

$$\\frac{m}{2}=28$$

Multiply both sides by $$2$$.

$$m=56$$

Final answer: $$56$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$56$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$72$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$76$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$112$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["geometry-and-trigonometry-lines-angles-and-triangles"],"date":"2026-06-04T09:04:49.836Z","modified":"2026-07-14T05:49:54.749Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L1b",null,{"targetType":"quiz","targetSlug":"psat-8-9-lines-angles-triangles-quiz-3"}]}]]}]}]]

Quiz 3

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