Lines, Angles, and Triangles on the SAT: Examples & Practice

Start line-and-angle problems with a named relationship

If adjacent angles form a straight line and measure $3 x + 10$ degrees and $2 x + 20$ degrees, then $3 x + 10 + 2 x + 20 = 180$ . Solving gives $x = 30$ , so the angles are 100 and 80 degrees.

Vertical angles are opposite angles formed by two intersecting lines; they are equal. Adjacent angles are not automatically equal. If parallel lines are stated, corresponding and alternate interior angles give additional equalities.

Keep triangle angle sums separate from line sums

A triangle has angles $x$ , $2 x$ , and 60 degrees. Their sum is 180 degrees, giving $3 x + 60 = 180$ and $x = 40$ . The three angles are 40, 80, and 60 degrees.

An exterior angle equals the sum of the two remote interior angles. In that triangle, the exterior angle next to the 60-degree angle is 120 degrees, matching $40 + 80$ .

Match corresponding vertices in similar triangles

If triangles $A BC$ and $D EF$ are similar in that order, $A$ matches $D$ , $B$ matches $E$ , and $C$ matches $F$ . If $A B = 6$ , $D E = 9$ , and $BC = 8$ , the scale factor is $\frac{9}{6} = \frac{3}{2}$ , so $EF = 12$ .

Match sides by vertices or angles rather than their visual location on the page. A rotated triangle keeps the same correspondence even when its longer side appears on a different edge.

Use given markings rather than an apparent shape

A triangle that looks isosceles needs equal-side or equal-angle evidence before you use that property. Equal sides imply equal opposite angles, and equal angles imply equal opposite sides.

For a line-and-angle miss, write the missing relationship. For a triangle miss, distinguish angle sum, exterior angle, isosceles, and similarity. These are separate setups even though they share one bank label.

Check your understanding

Try it yourself

A triangle has interior angles of 35 degrees and 65 degrees. What is the third angle?

A70 degreesB80 degreesC100 degreesD115 degrees

Choose an answer.

Sample lines, angles, and triangles questions

Lines, Angles, and Triangles · Easy

x

and

y

are supplementary angles, which of the following must be true?

y = 180 - x

y > 26

x = y

x + y > 180

Choose an answer.

Open the question and explanation

Lines, Angles, and Triangles · Easy

The measure of angle Z is 30°. What is the measure, in radians, of angle Z?

\frac{1}{12} π

\frac{1}{6} π

\frac{1}{3} π

\frac{5}{6} π

Choose an answer.

Open the question and explanation

Lines, Angles, and Triangles · Easy

The measure of angle

Y

6 0^{\circ}

. What is the measure, in radians, of angle

Y

\frac{2}{3} π

π

\frac{1}{6} π

\frac{1}{3} π

Choose an answer.

Open the question and explanation

Practice this skill

For angle questions, annotate the exact equality or 180-degree sum.
For triangle questions, write the vertex correspondence before a proportion.
Alternate line-angle and triangle drills so a picture alone does not choose the rule.

Practice lines, angles, and triangles

Print the lines, angles, and triangles worksheet and worked answers.

Then use a mixed practice module to check whether you can choose this method among other question types.

Source and question labels

The bank label for this guide is "Lines, angles, and triangles" in Geometry and Trigonometry. The worked examples above are written for this guide.

College Board: Types of Math tested

Start line-and-angle problems with a named relationship

Keep triangle angle sums separate from line sums

Match corresponding vertices in similar triangles

Use given markings rather than an apparent shape

Check your understanding

Sample lines, angles, and triangles questions

Practice this skill

Source and question labels

Related skills

Right Triangles and Trigonometry

Area and Volume

Circles