The measure of one acute angle of a right triangle is 12 more than 3 times the measure of the other acute angle. Find the measure of each acute angle

Question

How do I do this?

Answer 1

Let the measure of an acute angle be x, the measure of the other acute angle would then be 3x + 12.

 

The sum of all the angles of the right triangle would equal 180°.

 

(3x + 12) + x +90° = 180°

 

4x + 102 = 180

 

4x = 78

 

x = 19.5

 

 

Now substitute this value for x into the expressio for each angle.

 

70.5° and 19.5° are the measures of the two acute angles.