Answered

In triangle MNP the measure of angle NPM is 80⁰ and the measure of angle MNP is 22.5⁰. What is the measure of angle PMN in degrees?



Answer :

joluna323
To find the measure of angle PMN, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Given:
- Measure of angle NPM = 80 degrees
- Measure of angle MNP = 22.5 degrees

Let's denote the measure of angle PMN as x degrees.

So, the sum of the angles in triangle MNP is:

80 degrees (angle NPM) + 22.5 degrees (angle MNP) + x degrees (angle PMN) = 180 degrees

Now, we can solve for x:

80 + 22.5 + x = 180

102.5 + x = 180

Subtracting 102.5 from both sides:

x = 180 - 102.5

x = 77.5

So, the measure of angle PMN is 77.5 degrees.
sqdancefan

Answer:

  77.5°

Step-by-step explanation:

You want the measure of angle M in ∆MNP with angle P=80° and angle N=22.5°.

Angle sum

The angle sum theorem tells you the sum of the measures of the angles in a triangle is 180°. That means ...

  M + N + P = 180°

  M + 22.5° +80° = 180° . . . . . . . . . use the given values

  M = 180° -102.5° = 77.5° . . . . . . . subtract 102.5° from both sides

The measure of angle PMN is 77.5°.

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