The measure of ∠ABC is 124°, given that BX is an angle bisector to ∠ABC, and ∠XBC = 62°. Hence, 3rd option is the right choice.
What is an angle bisector?
A ray, segment, or line that splits a given angle into two equal angles is known as an angle bisector. When something is bisected, it is split into two equal sections. In geometry, an angle bisector is a line or ray that divides a triangle into two equal angles.
How to solve the question?
In the question, we are given that BX bisects ∠ABC, and are asked if the measure of ∠ABC is ∠XBC = 62°.
We assume the measure of ∠ABC to be x°.
As BX bisects ∠ABC, that is, BX is an angle bisector to ∠ABC, we know that ∠XBC = ∠XBA = 1/2 of ∠ABC = 1/2 of x° = (x/2)°.
Thus, ∠XBC = (x/2)°,
or, 62° = (x/2)°,
or, x = 62*2° = 124°.
Thus, the measure of ∠ABC is 124°, given that BX is an angle bisector to ∠ABC, and ∠XBC = 62°. Hence, 3rd option is the right choice.
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