Lines, angles, and triangles — SAT practice questions

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Practice 100 Lines, angles, and triangles questions in the app

What this topic is

Lines, angles, and triangles questions rely on a handful of facts: vertical angles are equal, angles on a straight line add to one hundred eighty degrees, and so do the interior angles of any triangle.

When a transversal crosses parallel lines, corresponding angles and alternate interior angles are equal. Many items write angle measures as expressions in x, which turns the geometry into a linear equation. Similar triangles have equal corresponding angles and proportional corresponding sides, so matching vertices in the stated order is essential; pairing the wrong sides gives a wrong ratio.

Measurements should come from the given information, since figures are not always drawn to scale.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

Two lines intersect, forming two pairs of vertical angles. One angle measures $(3 x + 15)^{\circ}$ , and its vertical angle measures $7 5^{\circ}$ . What is the value of $x$ ?

20✓ Correct25✗ Not this one75✗ Not this one105✗ Not this one

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Answer: A — 20

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

Question 2Easier

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

20✗ Not this one40✗ Not this one60✗ Not this one80✓ Correct

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Answer: D — 80

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

Question 3Easier

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

11.2✗ Not this one16✗ Not this one17.5✓ Correct22✗ Not this one

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Answer: C — 17.5

Similar triangles have proportional corresponding sides: $\frac{S T}{P Q} = \frac{T U}{Q R}$ , so $\frac{10}{8} = \frac{T U}{14}$ , giving $T U = 14 \cdot \frac{5}{4} = 17.5$ . The choice 11.2 uses the inverted scale $\frac{8}{10}$ . The choice 16 adds the side-length difference $10 - 8$ to $Q R$ . The choice 22 adds $P Q$ and $Q R$ instead of using the similarity ratio.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 100 Lines, angles, and triangles questions in the app

Lines, angles, and triangles — SAT practice questions

What this topic is

Sample questions

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Math