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:

∠MON = 99°

Step-by-step explanation:

Given a straight lime LON and a line Om intersecting LON at point O.

Sum of angle on a straight line is 180°

Given ∠MON = (8x−13)°

and ∠LOM =( 7x−17)°

Before we can get the value of angle ∠MON, first we need to get the value of x

Taking the sum of the two angles and equating to 180° we will have;

(8x−13)°+(7x−17)° = 180

Opening the bracket and collecting the like terms;

8x-13+7x-17 = 180°

8x+7x-13-17 = 180°

15x-30 = 180°

15x = 180+30

15x = 210°

x = 210/15

x = 14°

∠MONm = (8x−13)°

If x = 14°

∠MON = 8(14)-13

∠MON = 112-13

∠MON = 99°

Answer 2

Answer:

Step-by-step explanation:

From the data given,

∠MON=8x−13

∠LOM=7x−17

∠LON= is a straight line angle, i.e. it is 180°

Then, the sum of MON and LOM is equal to LON

∠MON + ∠LOM = ∠LON

8x-13 + 7x - 17 = 180

15x -30 = 180

15x = 180+30

15x =210

x =210/15

x = 14°

We want to find MON

∠MON=8x−13

∠MON=8(14)−13

∠MON=112−13

∠MON= 99°

Check attachment for diagram