Answer:
x=90 degrees and y=41 degrees.
Step-by-step explanation:
In the diagram
[tex]AB=AC\\$Therefore \triangle ABC$ is an isosceles triangle[/tex]
[tex]m\angle C=49^\circ[/tex]
Since ABC is Isosceles
[tex]m\angle B=m\angle C=49^\circ $ (Base angles of an Isosceles Triangle)[/tex]
[tex]m\angle A+m\angle B+m\angle C=180^\circ $ (Sum of angles in a Triangle)\\m\angle A+49^\circ+49^\circ=180^\circ\\m\angle A=180^\circ-(49^\circ+49^\circ)\\m\angle A=82^\circ[/tex]
[tex]m\angle x=90^\circ $(perpendicular bisector of the base of an isosceles triangle)[/tex]
[tex]m\angle y=m\angle A \div 2 $ (perpendicular bisector of the angle at A)\\m\angle y=82 \div 2\\m\angle y=41^\circ[/tex]
Therefore:
x=90 degrees and y=41 degrees.
