Question 22·Easy·Lines, Angles, and Triangles
In right triangle , is the right angle. If the measure of is , what is the measure of ?
For right-triangle angle questions, immediately use two facts: (1) the angles in any triangle sum to , and (2) the right angle is . Combine these to see that the two non-right angles in a right triangle must sum to , so you can quickly find the unknown acute angle by computing minus the given acute angle, usually doable in your head for speed.
Hints
Remember a key fact about triangles
What is the sum of the three interior angles in any triangle?
Use the right angle information
A right angle measures . If is right and is , write an equation for adding up to .
Isolate angle B
From your equation, combine the known angles into a single number and then solve for by subtracting from .
Desmos Guide
Use Desmos to verify the calculation
In the expression line, type 180 - 90 - 35 and look at the numerical result; this value is the measure of in degrees.
Step-by-step Explanation
Use the triangle angle sum
For any triangle, the measures of the three interior angles always add up to .
So in triangle :
Substitute the known angle measures
You are told that is a right angle, so , and .
Substitute these into the angle-sum equation:
Combine the known angles:
Solve for the unknown angle
Solve by subtracting from both sides:
So the measure of is , which corresponds to choice C.