Question

m∠LONm, angle, L, O, N is a straight angle.
m∠LOM=4x+30∘\qquad m \angle LOM = 4x + 30^\circm∠LOM=4x+30∘m, angle, L, O, M, equals, 4, x, plus, 30, degrees
m∠MON=8x+90∘\qquad m \angle MON = 8x + 90^\circm∠MON=8x+90∘m, angle, M, O, N, equals, 8, x, plus, 90, degrees
Find m∠MONm\angle MONm∠MONm, angle, M, O, N:

Answer 1

Given that LON is a straight line.

The measure of ∠LOM is (4x + 30)°

The measure of ∠MON is (8x + 90)°

We need to determine the measure of ∠MON

The value of x:

Since, LON is a straight line, then the angles LON and MON add upto 180°

Thus, we have;

$\angle LON+\angle MON= 180^{\circ}$

Substituting the values, we get;

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

            $12x+120=180$

                      $12x=60$

                         $x=5$

Thus, the value of x is 5.

Measure of ∠MON:

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

Thus, we have;

$\angle MON = (8(5)+90)^{\circ}$

$\angle MON = (40+90)^{\circ}$

$\angle MON =130^{\circ}$

Thus, the measure of ∠MON is 130°

Answer 2

Answer:

The answer is 130

Step-by-step explanation: