Question

In the figure above line m is parallel to line n.
If
m ∠ 1 = ( 4 x + 15 ) ∘
and
m ∠ 2 = ( 9 x + 35 ) ∘
, find

Answer 1

Given:

Line m is parallel to line n.

The measure of ∠1 is (4x + 15)°

The measure of ∠2 is (9x + 35)°

We need to determine the measure of ∠1

Value of x:

From the figure, it is obvious that ∠1 and ∠2 are linear pairs.

Thus, we have;

$\angle 1+\angle 2=180^{\circ}$

Substituting the measures of ∠1 and ∠2, we get;

$4x+15+9x+35=180$

             $13x+50=180$

                     $13x=130$

                        $x=10$

Thus, the value of x is 10.

Measure of ∠1:

The measure of ∠1 can be determined by substituting x = 10 in the measure of ∠1

Thus, we have;

$\angle 1 =4(10)+15$

    $=40+15$

$\angle 1=55^{\circ}$

Thus, the measure of ∠1 is 55°