In the triangle shown, the measures of the three interior angles are , , and . Which choice is the value of ?

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 4 | Free SAT Prep | Aniko

00:00

Question 4·Easy·Lines, Angles, and Triangles

0 / 50

In the triangle shown, the measures of the three interior angles are $40^\circ$ , $(a+20)^\circ$ , and $(3a)^\circ$ . Which choice is the value of $a$ ?

For triangle angle problems, immediately use the fact that interior angles sum to $180^\circ$ . Write one equation by adding the three angle expressions, then combine like terms and solve; keep track of constants and variable terms separately to avoid arithmetic mistakes.

Hints

Click me!

Triangle fact

Remember that the measures of the interior angles of any triangle add up to $180^\circ$ .

Write an equation

Add the three given angle expressions and set the sum equal to $180$ .

Combine terms carefully

Be sure to add the constants ( $40$ and $20$ ) and combine the $a$ terms ( $a$ and $3a$ ) correctly.

Desmos Guide

Enter the two sides of the equation

Graph $y=40+(x+20)+3x$ and graph $y=180$ .

Find the intersection

Click the intersection point of the two graphs and read the $x$ -coordinate. That value is $a$ .

Step-by-step Explanation

Set up the triangle angle-sum equation

The sum of the interior angles of a triangle is $180^\circ$ , so:

40 + (a+20) + 3a = 180

Simplify and solve

Combine like terms and solve:

40 + a + 20 + 3a = 180 \\[0.7em] 60 + 4a = 180 \\[0.7em] 4a = 120 \\[0.7em] a = 30

So, $a=30$ .

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation