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

Answer ( 1 )

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    2022-12-24T16:50:27+00:00
    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.
    Learn more about complementary angles here:
    brainly.com/question/5708372
    #SPJ2

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