right triangle has acute angles measuring 3x degrees and 2x + 10 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of the acute angles as A and B. We have:

A = 3x degrees

B = 2x + 10 degrees

Since we know that the triangle is a right triangle, one of the angles is a right angle, which has a measure of 90 degrees. Therefore, the sum of the angles of the triangle is:

A + B + 90 = 180 degrees

Substituting the given values:

3x + 2x + 10 + 90 = 180

5x + 100 = 180

Subtracting 100 from both sides of the equation:

5x = 80

Dividing both sides by 5:

x = 16

Now that we know the value of x, we can find the measure of the acute angles:

A = 3x = 3(16) = 48 degrees

B = 2x + 10 = 2(16) + 10 = 42 degrees

Therefore, the measures of the missing angles are 48 degrees and 42 degrees.