Question

Answer each question below.

14. In angle LMN, the exterior angle adjacent to angle L has a measure of 5x+12. If the measure of angle M= 3x-2 and the measure of angle N= 50. Find the measure of angle L.

Answer 1

`\huge\boxed{\sf L = 78\°}`

Explanation:

Given that:

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

Statement:

• Exterior angle is equal to the sum of non-adjacent interior angles.

So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.

Here,

Exterior angle of L = M + N

5x + 12 = 3x - 2 + 50

5x + 12 = 3x + 48

Subtract 12 to both sides

5x = 3x + 48 - 12

5x - 3x = 36

2x = 36

Divide 2 to both sides

x = 18

So,

Measure of angle M:

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

Measure of angle L:

We know that,

• Sum of all the interior angles of triangle is 180 degrees.

L + M + N = 180°

L + 52 + 50 = 180

L + 102 = 180

Subtract 102 to both sides

L = 180 - 102

L = 78°

`\rule[225]{225}{2}`