Question

What is the measure of angle LMP if m∠LMP=8x−12 and m∠PMN=4x+6?

A) 2x−3

B) 4x+6

C) 8x−12

D) 12x−18

Answer 1

The measure of angle LMP is 24.

Step-by-step explanation:

The measure of angle LMP can be obtained by setting the two given angle measures equal to each other and solving for x. We have:

8x - 12 = 4x + 6

Subtracting 4x from both sides, we get:

4x - 12 = 6

Adding 12 to both sides, we get:

4x = 18

Dividing both sides by 4, we get:

x = 4.5

Now we can substitute this value back into either equation to find the measure of angle LMP. Let's use m∠LMP = 8x - 12:

m∠LMP = 8(4.5) - 12

m∠LMP = 36 - 12

m∠LMP = 24

Therefore, the measure of angle LMP is 24.