The value of x is 36° and the value of y is 108°.
Solution:
Given data:
∠1 = 2x°, ∠2 = y° and ∠3 = 72°
Vertical angle theorem:
If two lines are intersecting at a point then vertically opposite angles are equal.
∠1 and ∠3 are vertically opposite angles.
⇒ ∠1 = ∠3
⇒ 2x° = 72°
Divide by 2 on both sides of the equation.
⇒ x° = 36°
Sum of the adjacent angles in a straight line = 180°
⇒ m∠2 + m∠3 = 180°
⇒ y° + 72° = 180°
⇒ y° = 180° – 72°
⇒ y° = 108°
Hence the value of x is 36° and the value of y is 108°.
