Question

If m
X=49, y=41

X=90, y= 49

X=41, y =49

X=90, y=41

Answer 1

x=90 degrees and y=41 degrees.

Explanation:

In the diagram

`AB=AC\\$Therefore \triangle ABC$ is an isosceles triangle`

`m\angle C=49^\circ`

Since ABC is Isosceles

`m\angle B=m\angle C=49^\circ $ (Base angles of an Isosceles Triangle)`

`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`

`m\angle x=90^\circ $(perpendicular bisector of the base of an isosceles triangle)`

`m\angle y=m\angle A / 2 $ (perpendicular bisector of the angle at A)\\m\angle y=82 / 2\\m\angle y=41^\circ`

Therefore:

x=90 degrees and y=41 degrees.