Question

The m∠B is two more than three times the measure of ∠C. If ∠B and ∠C are complementary angles, find the measures of both angles.

Answer 1

B = 68° and C = 22°

Explanation:

Let angle B's measure be B and angle C's measure be C.

Also note that complementary means that they sum to 90.

Now:

The m∠B is two more than three times the measure of ∠C:

we can write:

B = 3C + 2

If ∠B and ∠C are complementary angles:

B + C = 90

Putting 1st equation in 2nd, we get:

B + C = 90

3C + 2 + C = 90

4C = 90 - 2

4C = 88

C = 88/4 = 22

Now B = 3C + 2, so

B = 3(22) + 2 = 68

Hence, B = 68 degrees and C = 22 degrees