Part A:
Since angles OPQ and RPS are complementary, we have the equation:
m∠OPQ + m∠RPS = 90°
Substitute in the given angle measures:
(x + 17) + (8x - 8) = 90
Combine like terms:
9x + 9 = 90
Subtract 9 from both sides:
9x = 81
Divide by 9:
x = 9
Part B:
Using the value of x from Part A, we can find the measures of angles OPQ and RPS:
m∠OPQ = x + 17
m∠OPQ = 9 + 17
m∠OPQ = 26°
m∠RPS = 8x - 8
m∠RPS = 8(9) - 8
m∠RPS = 72 - 8
m∠RPS = 64°
Therefore, m∠OPQ = 26° and m∠RPS = 64°.
Part C:
Vertical angles are two pairs of opposite angles formed by intersecting lines. Since angles OPQ and RPS are not formed by intersecting lines, they cannot be vertical angles. Vertical angles will have equal measures, which is not the case for angles OPQ and RPS.
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)
1 answer
1 answer