In triangle , the measure of angle is and the measure of angle is . What is the measure, in degrees, of angle ?

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 28 | Free SAT Prep | Aniko

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Question 28·Easy·Lines, Angles, and Triangles

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In triangle $XYZ$ , the measure of angle $X$ is $35^{\circ}$ and the measure of angle $Y$ is $65^{\circ}$ . What is the measure, in degrees, of angle $Z$ ?

For triangle angle questions, immediately recall that the three interior angles add to $180^{\circ}$ . Write a simple equation where the known angles are added to an unknown for the missing angle, combine the known measures, and subtract this sum from $180^{\circ}$ . Doing the arithmetic carefully in one line (or using Desmos for a quick check) helps you avoid common mistakes like forgetting to include one angle or confusing the sum of known angles with the missing angle.

Hints

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Recall a key triangle fact

What do the measures of the three interior angles in any triangle always add up to?

Write an equation for the three angles

Let $m\angle Z$ be the unknown. Write an equation that adds $35^{\circ}$ , $65^{\circ}$ , and $m\angle Z$ and sets this sum equal to the total from the first hint.

Combine like terms and isolate the unknown

First add $35^{\circ}$ and $65^{\circ}$ , then subtract this sum from $180^{\circ}$ to find $m\angle Z$ .

Desmos Guide

Use Desmos to compute the missing angle

In Desmos, type 180 - 35 - 65 and press Enter. The value that appears is the measure of angle $Z$ in degrees.

Step-by-step Explanation

Use the triangle angle sum rule

Recall that in any triangle, the measures of the three interior angles always add up to $180^{\circ}$ . So for triangle $XYZ$ ,

m\angle X + m\angle Y + m\angle Z = 180^{\circ}

Substitute the known angle measures

You are given $m\angle X = 35^{\circ}$ and $m\angle Y = 65^{\circ}$ . Substitute these into the equation:

35^{\circ} + 65^{\circ} + m\angle Z = 180^{\circ}

Add the known angles:

35^{\circ} + 65^{\circ} = 100^{\circ}

So the equation becomes:

100^{\circ} + m\angle Z = 180^{\circ}

Solve for the measure of angle Z

To find $m\angle Z$ , subtract $100^{\circ}$ from $180^{\circ}$ :

m\angle Z = 180^{\circ} - 100^{\circ} = 80^{\circ}

So, the measure of angle $Z$ is $80^{\circ}$ .

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