Find the valuable of each variable.

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°.

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