Given is a right angle, find the measurement of .
A) 70°
B) 55°
C) 110°
D) 35°
E) 45°

Question

Given  is a right angle, find the measurement of  . 
A) 70° 
B) 55° 
C) 110° 
D) 35° 
E) 45°

Quizplus · Accepted Answer

Since the given angle 11eb69da_9ee6_9315_af94_5501b1ba0c2c_TB8311_11 is a right angle, it equals 90°.

Let's label the other two angles in the triangle as A and B. 
So we have: 
Angle 11eb69da_9ee6_ba26_af94_71c45ce9f435_TB8311_11 = A 
Angle 11eb69da_9ee6_ba27_af94_d916547661b5_TB8311_00 = B

Using the fact that the angles in a triangle add up to 180°, we can write:

A + 90° + B = 180° 
A + B = 90°

Thus, both angle A and angle B are acute angles (less than 90°).

Since we know that angle 11eb69da_9ee6_9315_af94_5501b1ba0c2c_TB8311_11 is a right angle, it is larger than angle A. Therefore, angle B must be smaller than angle A.

Since the sum of the angles in a triangle is 180° and angle 11eb69da_9ee6_9315_af94_5501b1ba0c2c_TB8311_11 is 90°, the sum of angles A and B must be 90°.

So, we conclude that angle B is smaller than angle A and the sum of the two angles is 90°. The only answer choice that fits this requirement is D) 35°.

Given Is a Right Angle, Find the Measurement of