Question

Given \qquad m \angle LONm∠LONm, angle, L, O, N is a straight angle. \qquad m \angle MON = 8x - 13^\circm∠MON=8x−13 ∘ m, angle, M, O, N, equals, 8, x, minus, 13, degrees \qquad m \angle LOM = 7x - 17^\circm∠LOM=7x−17 ∘ m, angle, L, O, M, equals, 7, x, minus, 17, degrees Find m\angle MONm∠MONm, angle, M, O, N:

Answer 1

Answer:

$\boxed{99°}$

Step-by-step explanation:

m<MON = 8x - 13°

m<LOM = 7x - 17°

To find : m <MON

First, we have to find the value of x :

Create an equation

$\mathrm{8x - 13 + 7x - 17 = 180}$ ( sum of angle in straight line )

Collect like terms

$\mathrm{15x - 13 - 17 = 180}$

Calculate

$\mathrm{15x - 30 = 180}$

Move constant to R.H.S and change its sign

$\mathrm{15x = 180 + 30}$

Calculate the sum

$\mathrm{15x = 210}$

Divide both sides of the equation by 15

$\mathrm{ \frac{15x}{15} = \frac{210}{15} }$

Calculate

$\mathrm{x = 14}$

Now, let's find the value of m<MON

$\mathrm{8x - 13}$

Plug the value of x

$\mathrm{ = 8 \times 14 - 13}$

Calculate the product

$\mathrm{ = 112 - 13}$

Calculate the difference

$\mathrm{ = 99}$ °

Hope I helped!

Best regards!