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

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 34 | Free SAT Prep | Aniko

00:00

Question 34·Easy·Lines, Angles, and Triangles

0 / 50

In $\triangle ABC$ , $\angle A$ measures $42^{\circ}$ and $\angle B$ measures $53^{\circ}$ . What is the measure, in degrees, of $\angle C$ ?

For triangle angle questions, immediately recall that the three interior angles sum to 180°. Write a quick equation like $\text{known angle 1} + \text{known angle 2} + x = 180$ , combine the known angles mentally, and subtract from 180 to find the missing angle. Doing the arithmetic carefully but quickly—often in two short steps (add, then subtract)—helps avoid mistakes and saves time on the SAT.

Hints

Click me!

Recall a key triangle fact

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

Write an equation for the angles

Let $\angle C$ be the unknown. Write an equation that adds $\angle A$ , $\angle B$ , and $\angle C$ and sets their sum equal to 180°.

Use basic arithmetic to isolate $\angle C$

After substituting $42^{\circ}$ and $53^{\circ}$ into your equation, combine those two numbers, then subtract that sum from 180 to get $\angle C$ .

Desmos Guide

Compute the missing angle with Desmos

In the Desmos calculator, type 180 - 42 - 53 and press Enter. The numerical result shown is the measure of $\angle C$ 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 $180^{\circ}$ . For $\triangle ABC$ , this means:

\angle A + \angle B + \angle C = 180^{\circ}

Substitute the known angle measures

You are given $\angle A = 42^{\circ}$ and $\angle B = 53^{\circ}$ . Substitute these into the equation:

42^{\circ} + 53^{\circ} + \angle C = 180^{\circ}

Now combine the known angles:

42^{\circ} + 53^{\circ} = 95^{\circ}

So the equation becomes:

95^{\circ} + \angle C = 180^{\circ}

Solve for the missing angle

To isolate $\angle C$ , subtract $95^{\circ}$ from both sides of the equation:

\angle C = 180^{\circ} - 95^{\circ}

Compute the difference: $180 - 95 = 85$ , so $\angle C$ measures $85^{\circ}$ . Thus, the correct answer choice is B) 85.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation