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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:

Given qquad m angle LONmLONm angle L O N is a straight angle qquad m angle MON 8x 13circmMON8x13 m angle M O N equals 8 x minus 13 degrees qquad m angle LOM 7x class=

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TheAnimeGirl

Answer:

[tex] \boxed{99°}[/tex]

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

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

Collect like terms

[tex] \mathrm{15x - 13 - 17 = 180}[/tex]

Calculate

[tex] \mathrm{15x - 30 = 180}[/tex]

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

[tex] \mathrm{15x = 180 + 30}[/tex]

Calculate the sum

[tex] \mathrm{15x = 210}[/tex]

Divide both sides of the equation by 15

[tex] \mathrm{ \frac{15x}{15} = \frac{210}{15} }[/tex]

Calculate

[tex] \mathrm{x = 14}[/tex]

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

[tex] \mathrm{8x - 13}[/tex]

Plug the value of x

[tex] \mathrm{ = 8 \times 14 - 13}[/tex]

Calculate the product

[tex] \mathrm{ = 112 - 13}[/tex]

Calculate the difference

[tex] \mathrm{ = 99}[/tex] °

Hope I helped!

Best regards!

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