Question

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? A) 17° B) 23° C) 27° D) 31°

Answer 1

A. ∠ QPR = 17°

Explanation:

From the given information, let QP be the length of the ramp.

Then, ∠ QPR is the angle between the ramp and the ground.

∠ PQR is the angle between the ramp and the doorpost and

∠ QRP is the angle between the doorpost and the ground.

Clearly, ∠ PQR = 73° (given)

∠ QRP = 90° (since doorpost and the ground are perpendicular to each other)

Now, use triangle sum propoerty of ΔQPR, we get,

∠ QPR + ∠ PQR + ∠ QRP = 180°

∠ QPR + 73 + 90 = 180°

∠ QPR + 163 = 180°

∠ QPR = 180 - 163

∠ QPR = 17°