Question

Given that LMN and PQR are
complementary angles, find the measures
of the angles if the m LMN = 8x + 1 and
the m PQR = 2x + 9.

Answer 1

Answer:

∠ LMN = 65° , ∠ PQR = 25°

Step-by-step explanation:

Complementary angles sum to 90°

∠ LMN + ∠ PQR = 90° , that is

8x + 1 + 2x + 9 = 90

10x + 10 = 90 ( subtract 10 from both sides )

10x = 80 ( divide both sides by 10 )

x = 8

Then

∠ LMN = 8x + 1 = 8(8) + 1 = 64 + 1 = 65°

∠ PQR = 2x + 9 = 2(8) + 9 = 16 + 9 = 25°