Question 2·Medium·Lines, Angles, and Triangles

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In $\triangle XYZ$ , $m\angle X = 30^\circ$ and $m\angle Y = 45^\circ$ . What is $m\angle Z$ , in degrees? (Disregard the degree symbol when entering your answer.)

Your answer

For triangle angle questions, immediately recall that the three interior angles sum to $180^\circ$ . Write a simple equation where you add the known angles plus a variable for the unknown angle and set the sum equal to 180, then solve by combining like terms and subtracting from 180. Doing this quickly in 1–2 steps helps avoid overthinking and reduces arithmetic mistakes.

Hints

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Recall a key triangle fact

What is the sum of the measures of the three interior angles in any triangle?

Introduce a variable for the unknown angle

Let $m\angle Z = z$ . How can you write an equation that adds $30$ , $45$ , and $z$ and sets that sum equal to the total from the first hint?

Solve the equation step by step

First add $30$ and $45$ . Then subtract that total from $180$ to isolate $z$ .

Desmos Guide

Compute the missing angle with an expression

In Desmos, type 180 - 30 - 45 and look at the numerical result. That value is the measure of angle Z in degrees.

Step-by-step Explanation

Use the triangle angle sum rule

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

Write an equation for angle Z

You are given $m\angle X = 30$ and $m\angle Y = 45$ . Let $m\angle Z = z$ . Substitute into the angle sum equation:

30 + 45 + z = 180

Combine the known angles:

75 + z = 180

Solve for the missing angle

Solve the equation $75 + z = 180$ by subtracting $75$ from both sides:

z = 180 - 75 = 105

So $m\angle Z = 105$ degrees.

Question 2·Medium·Lines, Angles, and Triangles

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation