Question

Triangle KNM is isosceles, where angle N is the vertex. What is the measure of angle K?

A) 110
B) 25°
C) 50°
D) 65°

Answer 1

In an isosceles triangle, the measure of angle K is equal to the measure of angle M. By setting up an equation and solving for x, we find that the measure of angle K is 60 degrees.

Step-by-step explanation:

In an isosceles triangle, the two base angles are equal. Since angle N is the vertex, the two base angles are angle K and angle M. Therefore, the measure of angle K is equal to the measure of angle M.

Let's denote the measure of angle K as x. Then, the measure of angle M is also x. Since the sum of the angles in a triangle is 180 degrees, we can write the equation:

x + x + angle N = 180.

Since triangle KNM is isosceles, angle N is x degrees. Thus, we can rewrite the equation:

2x + x = 180.

Combining like terms, we get:

3x = 180.

Dividing both sides by 3, we find:

x = 60.

Therefore, the measure of angle K is 60 degrees.