Question

Suppose that AKL M is isosceles with base MK.

Suppose also that m 2 M= (3x+36) and m 2 K = (4x +31)
Find the degree measure of each angle in the triangle.
m ZK = 0
m 2L =
m ZM =
MA
K
(3x +36)
(4x +31).
Х

Answer 1

m<K = 51°

m<L = 78°

m<M = 51°

Explanation:

Base angles of an isosceles ∆ are equal to each other, therefore,

m<M = m<K

Substitute

3x + 36 = 4x + 31

Collect like terms and solve for x

3x - 4x = -36 + 31

-x = -5

Divide both sides by -1

x = 5

Let's find each degree measure using the value of x

m<K = 4x + 31

Plug in the value of x

m<K = 4(5) + 31

m<K = 20 + 31

m<K = 51°

m<M = 3x + 36

= 3(5) + 36

= 15 + 36

m<M = 51°

m<L = 180° - (m<M + m<K) (sum of triangle theorem)

Substitute

m<L = 180 - (51 + 51)

m<L = 78°