Calculate the measure of ∠ PMU and ∠ UPM.

m∠ PMU =
m∠ UPM =

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

Step-by-step explanation:

justin bieber ml.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°