The ramp in the picture makes an angle of 73° with the doorpost.
What is the measure of the angle ∠QPR, between the ramp and the ground, if angle ∠RQP is a right angle?
Responses
A 17°17°
B 31°31°
C 36°36°
D 23°23°
E 27°
Since angle RQP is a right angle, we know that angle QPR is complementary to angle PQR. Therefore, angle QPR is 90° - 73° = 17°.
Answer: A) 17°
To find the measure of angle ∠QPR, we can use the fact that the sum of the angles in a triangle is 180°.
Given that angle ∠RQP is a right angle (90°) and angle ∠QPR is the angle we need to find, we can use the equation:
∠QPR + ∠RQP + ∠Q = 180°
Substituting the given values, we have:
∠QPR + 90° + 73° = 180°
Combining like terms, we get:
∠QPR + 163° = 180°
To isolate ∠QPR, we subtract 163° from both sides of the equation:
∠QPR = 180° - 163°
∠QPR = 17°
Therefore, the measure of angle ∠QPR, between the ramp and the ground, if angle ∠RQP is a right angle, is 17°.
The correct answer is A) 17°.