One acute angle of a right triangle is 16 degrees smaller than the other. Find the larger acute angle of this triangle.

The angles in any triangle add up to 180 °. We know that the triangle is rectangular, so one of the angles is 90 °.

Let us express the smaller unknown acute angle in terms of x °;

Then: (x + 16) ° is the larger unknown acute angle;

Let’s compose and solve the equation of the sum of angles in a triangle:

x ° + (x + 16) ° + 90 ° = 180 °;

x + x + 16 + 90 = 180;

2x + 16 + 90 = 180;

2 x + 106 = 180;

2x = 180 – 106;

2x = 74;

x = 74/2;

x = 37 ° – smaller acute angle;

x + 16 ° = 37 ° + 16 ° = 53 ° – greater acute angle.

Answer: 53 °