In triangle MNP the interior angle at N is 24 degrees and the exterior angle at P is 55 degrees. Which is the measure of the interior angle at M
if exterior is 55 the interior there is 180 - 55 = 125
125 + 24 + M = 180
M = 31
To find the measure of the interior angle at M in triangle MNP, we can use the fact that the sum of all interior angles in a triangle is always 180 degrees.
In this case, we know the measure of angle N is 24 degrees, and the measure of the exterior angle at P is 55 degrees.
Since the exterior angle at P is the sum of the remote interior angles at N and M, we can find the measure of the interior angle at M by subtracting the measure of angle N from the exterior angle at P.
Thus, the measure of the interior angle at M is:
Measure of interior angle at M = Measure of exterior angle at P - Measure of angle N
Measure of interior angle at M = 55 degrees - 24 degrees
Measure of interior angle at M = 31 degrees
Therefore, the measure of the interior angle at M in triangle MNP is 31 degrees.
To find the measure of the interior angle at M, we can use the fact that the sum of the interior angles in a triangle is always 180 degrees.
Step 1: Determine the measure of the exterior angle at M.
Since the interior angles at each vertex of a triangle form a linear pair with the corresponding exterior angles, the exterior angle at M is equal to the sum of the interior angle at M and the interior angle at N. Therefore, the exterior angle at M is (180 - 24) = 156 degrees.
Step 2: Calculate the measure of the interior angle at M.
The interior angle at M is the supplement of the exterior angle at M. The supplement of an angle is the angle that, when added to the given angle, gives a sum of 180 degrees.
Since the exterior angle at M is 156 degrees, the interior angle at M is (180 - 156) = 24 degrees.
Therefore, the measure of the interior angle at M is 24 degrees.