Question

Calculate the measure of ∠ PMU and ∠ UPM.

m∠ PMU =
m∠ UPM =

Answer 1

The Exterior Angle Theorem states that the measure of the exterior angle of a triangle is

equal to the sum of the measures of the two remote interior angles of the triangle. Angle

PMU is an exterior angle to nPBM and its corresponding remote interior angles are /PBM

and /BPM. So, I can calculate the sum of those two angle measures to find the measure

of /PMU

Explanation:

Answer 2

The value of m∠ PMU = 97 degrees

The value of m∠ UPM = 124 degrees

Given:

PUM = 62 degrees

MPB = 21 degrees

PBM = 35 degrees

To find the measure of ∠ PMU:

We can use the fact that the angles in a triangle add up to 180 degrees.

∠ PMU + ∠ PUM + ∠ MPB = 180 degrees

Substituting the given values:

∠ PMU + 62 degrees + 21 degrees = 180 degrees

∠ PMU = 180 degrees - 62 degrees - 21 degrees

∠ PMU = 97 degrees

To find the measure of ∠ UPM:

We can use the fact that the angles in a triangle add up to 180 degrees.

∠ UPM + ∠ PBM + ∠ MPB = 180 degrees

Substituting the given values:

∠ UPM + 35 degrees + 21 degrees = 180 degrees

∠ UPM = 180 degrees - 35 degrees - 21 degrees

∠ UPM = 124 degrees

Therefore:

m∠ PMU = 97 degrees

m∠ UPM = 124 degrees