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2 years ago

Answer each question below.

Mathematics

1 answer:

HACTEHA [7]2 years ago

7 0

Answer:

$\huge\boxed{\sf L = 78\°}$

Step-by-step explanation:

<h3><u>Given that:</u></h3>

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

<h3><u>Statement:</u></h3>

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,

<h3><u>Measure of angle M:</u></h3>

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

<h3><u>Measure of angle L:</u></h3>

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°

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

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