Comparison of Angles in a Triangle

Consider a triangle ABC where the interior angles of the triangle are given as follows:

Angle A measures $60^{ ext{o}}$ and is adjacent to angles B and C. Angle B measures $x^{ ext{o}}$, and angle C measures $y^{ ext{o}}$. The triangle ABC also possesses a line segment AD where D is a point on side BC such that the segment AD bisects angle A.

Determine the relationship between the measure of angle B (Quantity A) and the measure of angle C (Quantity B).

Note that the sum of the angles in any triangle is $180^{ ext{o}}$. Hence, we can express the measures of angles B and C as:

$x + y + 60^{ ext{o}} = 180^{ ext{o}}$

From this equation, find expressions for angles B and C.