Question

Suppose that LMN is isosceles with base ML

Suppose also that m 2 M = (2x +36)" and m 2 N = (5x + 27)
Find the degree measure of each angle in the triangle,
1-(5x + 27)
m 265
m2M - C
m2
1
M
(2x + 36)
X
Check

Answer 1

The degree measure of each angle in the triangle are m∠M = 54°, m∠L = 54°, m∠N = 72°

What is an isosceles triangle?

An Isosceles triangle is a triangle whose bases angles are congruent. By the word congruent, it means the same angles. The sum of angles in an Isosceles triangle is 180°.

Given that:

m∠M = (2x+36)°

Since the base angles are ∠M and ∠L, we can say;

• m∠M = m∠L = (2x+36)° (base angles of an isosceles triangle are equal)

Therefore, the sum of angles in an isosceles triangle is equal to 180°. i.e.

(2x + 36) + (2x + 36) + (5x + 27) = 180°

9x + 99 = 180

9x = 180 - 99

9x = 81

x = 81/9

x = 9

m∠M = m∠L = (2x+36)°

m∠M = m∠L = (2(9)+36)°

m∠M = m∠L = 54°

m∠N = 180° - (54° + 54°)

m∠N = 72°

Answer 2

m∠M = 54°

m∠N = 72°

m∠L = 54°

Explanation:

In the figure attached,

ΔLMN is an isosceles triangle having sides MN ≅ NL

Therefore, angles opposite to these sides will be equal in measure.

m∠M ≅ m∠L ≅ (2x + 36)°

Since, m∠M + m∠N + m∠L = 180°

(2x + 36)° + (5x + 27)° + (2x + 36)° = 180°

9x + 99 = 180

9x = 180 - 99

x =
`(81)/(9)`

x = 9

Therefore, m∠L = m∠M = (2x + 36)° = (2×9) + 36

= 54°

And m∠N = (5x + 27) = (5×9) + 27

= 72°