Question

XY bisects ∠AXB. If ∠YXB = 37.5o, what is the measure of ∠AXB?

Answer 1

Given,

XY bisects ∠AXB

The measure of ∠YXB= 37.5°

To find,

The measure of ∠AXB.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If a line bisects any angle, then it divided the two angles equally into 2 angles.{Statement-1}

Now, according to the question and statement-1;

XY bisects ∠AXB

=> ∠AXY = ∠YXB

And, according to the question, ∠YXB= 37.5°

=> ∠AXY = ∠YXB = 37.5°

{Equation-1}

Now, the measure of ∠AXB

= (the measure of ∠AXY) + (the measure of ∠YXB)

= 37.5° + 37.5°

{according to equation-1}

= 75°

=> the measure of ∠AXB = 75°

Hence, the measure of ∠AXB is equal to 75°.