# Lines, Angles, and Triangles on the SAT: Examples & Practice Source: https://1600.now/sat-skill/lines-angles-triangles --- Math · Geometry and Trigonometry ## Lines, Angles, and Triangles Name the geometric relationship before writing an equation. Vertical angles are equal, a straight angle totals 180 degrees, triangle interiors total 180 degrees, and similar triangles have proportional corresponding sides. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Start line-and-angle problems with a named relationship If adjacent angles form a straight line and measure $3x+10$ degrees and $2x+20$ degrees, then $3x+10+2x+20=180$. 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 $x$, $2x$, and 60 degrees. Their sum is 180 degrees, giving $3x+60=180$ 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 $ABC$ and $DEF$ are similar in that order, $A$ matches $D$, $B$ matches $E$, and $C$ matches $F$. If $AB=6$, $DE=9$, and $BC=8$, the scale factor is $\frac96=\frac32$, 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? A 70 degrees B 80 degrees C 100 degrees D 115 degrees ### Sample lines, angles, and triangles questions Lines, Angles, and Triangles · Easy If $x$ and $y$ are supplementary angles, which of the following must be true? A $y = 180 - x$ B $y \gt 26$ C $x = y$ D $x + y \gt 180$ - [Open the question and explanation](https://1600.now/bank/math/2934ff30) Lines, Angles, and Triangles · Easy The measure of angle Z is 30°. What is the measure, in *radians*, of angle Z? A $\frac{1}{12} \pi$ B $\frac{1}{6} \pi$ C $\frac{1}{3} \pi$ D $\frac{5}{6} \pi$ - [Open the question and explanation](https://1600.now/bank/math/a9a7cbf4) Lines, Angles, and Triangles · Easy The measure of angle $Y$ is $60^\circ$. What is the measure, in *radians*, of angle $Y$? A $\frac{2}{3}\pi$ B $\pi$ C $\frac{1}{6}\pi$ D $\frac{1}{3}\pi$ - [Open the question and explanation](https://1600.now/bank/math/f4d8b8c4) ### Practice this skill 1. For angle questions, annotate the exact equality or 180-degree sum. 2. For triangle questions, write the vertex correspondence before a proportion. 3. Alternate line-angle and triangle drills so a picture alone does not choose the rule. [Practice lines, angles, and triangles](https://1600.now/bank/math/skill/Lines%2C%20angles%2C%20and%20triangles) [Print the lines, angles, and triangles worksheet and worked answers](https://1600.now/sat-lines-angles-triangles-worksheet). Then use a [mixed practice module](https://1600.now/modules) 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](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Right Triangles and Trigonometry](https://1600.now/sat-skill/right-triangles-and-trig)** Locate the right angle first. - **[Area and Volume](https://1600.now/sat-skill/area-and-volume)** Choose the formula for the requested quantity, then identify its perpendicular height and units. - **[Circles](https://1600.now/sat-skill/circles)** Read a circle's radius before using area or circumference.