Question

M∠LONm, angle, L, O, N is a straight angle.

m
∠
L
O
M
=
4
x
+
3
0
∘
m∠LOM=4x+30
∘
m, angle, L, O, M, equals, 4, x, plus, 30, degrees
m
∠
M
O
N
=
8
x
+
9
0
∘
m∠MON=8x+90
∘
m, angle, M, O, N, equals, 8, x, plus, 90, degrees
Find
m
∠
M
O
N
m∠MONm, angle, M, O, N:

Answer 1

Given:

It is given that LON is a straight line. The measure of ∠LOM = (4x + 30)° and the measure of ∠MON = (8x + 90)°

We need to determine the value of m∠MON

Value of x:

Since, LON is a straight line and the angles LOM and MON are linear pairs of angles.

Since, linear pair of angles add up to 180°

Thus, we have;

`\angle LOM+\angle MON=180^(\circ)`

Substituting the values, we get;

`4x+30+8x+90=180`

`12x+120=180`

`12x=60`

`x=5`

Thus, the value of x is 5.

Value of m∠MON:

The measure of ∠MON can be determined by substituting x = 5 in the expression (8x + 90)°, we have;

`m\angle MON=(8(5)+90)^(\circ)`

`m\angle MON=(40+90)^(\circ)`

`m\angle MON=130^(\circ)`

Thus, the measure of ∠MON is 130°