Question 4·Easy·Lines, Angles, and Triangles

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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.

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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, $a=30$ .

Question 4·Easy·Lines, Angles, and Triangles

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation