Question

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

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°