Question

Find the value of x and y in the following figures:
Please do it fast with full explanation ​

Answer 1

$\large\bf\red{ii) x= 60°, y= 60°}$

$\large\bf\blue{ii) x= 130°, y= 50°}$

Hope it helps you!

Answer 2

For 1st part

ABC is a isosceles triangle

So angle y = angle ACB

Angle y + Angle ACB = 180° ( linear pair )

Angle ACB = 180°-120° = 60°

So angle y also = 60°

Angle x + Angle y = 120°. ( exterior angle sum theorem )

Angle x = 120°-60°

Angle x + 60° = 120°

Angle x = 60°

For part ii)

Here Angle BAC = 80° ( vertically opposite angles )

Angle y + Angle ACB + Angle BAC = 180° ( sum of angles of ∆ )

Angel y + Angle ACB = 180°-80° = 100°

But Angle y = Angle ACB ( Isosceles ∆ )

Angle y = 100°/2 = 50° ( Angle ACB also 50° )

Angle ACB + Angle x = 180° ( linear pair )

50° + Angle x = 180°

Angle x = 180°-50°

= 130 °