Question

Angles OPQ and RPS have the following measures: m∠OPQ = (x + 17)°, m∠RPS = (8x − 8)° Part A: If angle OPQ and angle RPS are complementary angles, find the value of x. Show every step of your work. (4 points) Part B: Use the value of x from Part A to find the measures of angles OPQ and RPS. Show every step of your work. (4 points) Part C: Could the angles also be vertical angles? Explain. (4 points)

Answer 1

A: x = 9°

B: m∠OPQ = 26°

m∠RPS = 64°

C: yes

Explanation:

A:

the complementary angles add up to measure 90°

i.e.

m∠OPQ + m∠RPS = 90°

x + 17 + 8x - 8 = 90

9x + 9 = 90

9x = 90 - 9

9x = 81

x = 81/9 = 9°

B:

m∠OPQ = (x + 17)° = 9 + 17 = 26°

m∠RPS = (8x - 8)° = 8(9) - 8 = 72 - 8 = 64°

C:

yes the complementary angles could also be the vertical angles.