The measure of angle M in triangle KMN is 64 degrees.
To find the measure of angle M, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Since triangle KMN is isosceles, the base angles KNL and LNM are congruent.
Therefore, we can set the two expressions representing these angles equal to each other:
(5x + 4) = (7x - 20)
Now, solve for x by combining like terms and isolating x:
2x = 24
x = 12
Substitute x = 12 back into either equation to find the measure of angle LNM:
LNM = 7(12) - 20
LNM = 64 degrees
Since angle M is the vertex angle of an isosceles triangle, it is congruent to angle LNM.
Therefore, the measure of angle M is 64 degrees, so the answer is A. 64⁰
The probable question may be:
Triangle KMN is isosceles, where angle N is the vertex.
KNL= (5x + 4) LNM= (7x- 20)
What is the measure of angle M?
A. 64⁰
B. 128⁰
C.52⁰
D. 26⁰ M