## Angles OPQ and RPS have the following measures: m∠OPQ = (x + 17)°, m∠RPS = (8x − 8)° Part A: If angle OPQ

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)

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2 weeks 2022-12-24T16:49:14+00:00 1 Answer 0 views 0

1. The value of x is 9.  The measures of angles are m∠OPQ = 26°, and m∠RPS = 64°.  The given angles also are vertical angles.

### What are complementary angles?

The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles.
Angles OPQ and RPS have the following measures:
m∠OPQ = (x + 17)°, m∠RPS = (8x − 8)°
Given that angle, OPQ and angle RPS are complementary angles,
Here, the pairing of angles sums up to 90° then they are called complementary angles.
So m∠OPQ + m∠RPS = 90°
⇒ (x + 17)° + (8x − 8)° = 90°
⇒9x + 9 = 90°
⇒ 9x = 81
⇒ x = 81/9
⇒ x = 9
Therefore, the value of x is 9.
Now, substitute the value of x = 9 in the angles OPQ and RPS.
m∠OPQ = (9 + 17)°, and  m∠RPS = (8(9) − 8)°
m∠OPQ = 26°, and  m∠RPS = 64°
The given angles also are vertical angles.
Thus, the value of x is 9.  The measures of angles are m∠OPQ = 26°, and m∠RPS = 64°. The given angles also are vertical angles.