In a right triangle, the acute angles measure x+15 and 2x degrees. What is the measure of the larger acute angle of the triangle?

15

25

40

50

Question

In a right triangle, the acute angles measure x+15 and 2x degrees. What is the measure of the larger acute angle of the triangle?


15

25

40

50

jadeishere · Answer

The angles in a triangle sum to 180 degrees. So as the right angle is 90, the other two must total 180 - 90 = 90. 

 So, x+15 + 2x = 90 
 Therefore 3x = 90 - 15 = 75 
 and so x=25. 

 So the smaller angles are x+15 = 40 degrees and 2x=50 degrees. 
 So the larger one is 50 degrees.