question_answer

A triangle ABC is inscribed in a circle, and the bisectors of the angles meet the circumference at X, Y, Z. The angles of the triangle X, Y, Z are respectively

A)  \[{{25}^{o}}\]

B)  \[{{25}^{o}}\]

C)  \[{{40}^{o}}\]

D)  \[{{50}^{o}}\]

Correct Answer: A

Solution :

Clearly, \[\angle BED={{120}^{o}}\] Also \[\angle ABD\] (the angles in same segment). Hence, \[{{15}^{o}}\] \[{{30}^{o}}\] \[{{45}^{o}}\] Similarly, other angles are \[{{60}^{o}}\]and \[\angle CAD={{40}^{o}}\].