Find the missing angles and give reason

Q1.

x = 83°

y = 79°

Q2.

x = 36°

y = 108°

Step-by-step explanation:

Q1.

Since, measure of exterior angle is equal to the measure of interior opposite angle.

Therefore,

x = 83°

y = 79°

Q2.

Since, y is the measure of exterior angle of the isosceles triangle, hence, by exterior theorem:

y = 54° + 54°

y = 108°

Since, x is the measure of the interior angle of the isosceles triangle.

Thus, by interior angle sum postulate of a triangle:

x + x + y = 180°

2x + 108° = 180°

2x = 180° - 108°

2x = 72°

x = 72°/2

x = 36°