In a right triangle, one acute angle is 22 degrees less than 3 times the other acute angle. What is the measure of the larger acute angle

The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is .
Additionally, the Right Triangle Acute Angle Theorem states that the two non-right angles in a right triangle are acute; that is to say, the right angle is always the largest angle in a right triangle.

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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