Lines, angles, and triangles — SAT practice questions

On the SAT Math test, Lines, angles, and triangles covers intersecting lines, vertical angles, interior angles of a triangle, and similar triangles. A student has to write an equation from an angle relationship, solve for an unknown, and use corresponding sides of similar triangles to find a missing length. Items often give expressions such as 3x+15 for an angle or a labeled similarity correspondence, then ask for x, a degree measure, or a side length. Traps include treating adjacent angles as vertical and matching sides that do not correspond. Choices are typically a single number.

Section: Math 44 questions on the paper
98 practice questions in the app

Sample questions

Question 1

Two lines intersect, forming two pairs of vertical angles. One angle measures $(3x+15)^\circ$ , and its vertical angle measures $75^\circ$ . What is the value of $x$ ?

A20
B25
C75
D105

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Answer: A — 20

Vertical angles are equal, so $3x+15=75$ , which gives $3x=60$ and $x=20$ .

Question 2

The three interior angles of a triangle measure $2x^\circ$ , $3x^\circ$ , and $4x^\circ$ . What is the measure, in degrees, of the largest angle?

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Answer: D — 80

The angles sum to 180: $2x+3x+4x=180$ , so $9x=180$ and $x=20$ . The largest angle is $4(20)=80$ .

Question 3

Triangle $PQR$ is similar to triangle $STU$ , with $P$ corresponding to $S$ , $Q$ corresponding to $T$ , and $R$ corresponding to $U$ . If $PQ=8$ , $QR=14$ , and $ST=10$ , what is the length of $TU$ ?

A11.2
B16
C17.5
D22

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Answer: C — 17.5

Similar triangles have proportional corresponding sides: $\dfrac{ST}{PQ}=\dfrac{TU}{QR}$ , so $\dfrac{10}{8}=\dfrac{TU}{14}$ , giving $TU=14\cdot\dfrac{5}{4}=17.5$ . The choice 11.2 uses the inverted scale $\dfrac{8}{10}$ . The choice 16 adds the side-length difference $10-8$ to $QR$ . The choice 22 adds $PQ$ and $QR$ instead of using the similarity ratio.

Practice 98 Lines, angles, and triangles questions in the app

Lines, angles, and triangles — SAT practice questions

Sample questions

More SAT topics

Math