Find the value of x.
(ANSWER IMMEDIATELY)

The value of x° is 90°.

Solution:

Given AC and BD are intersecting lines.

O is the point of intersection.

∠AOB and ∠COD are vertically opposite angles.

Given ∠AOB = (130 – x)° and ∠COD = (x – 50)°

To find the value of x:

Vertical angle theorem:

If two angles are vertically opposite then the angles are congruent.

⇒ ∠COD = ∠AOB

⇒ (x – 50)° = (130 – x)°

⇒ x° – 50° = 130° – x°

Add 50° on both side of the equation, by addition property of equality.

⇒ x° – 50°  + 50° = 130° – x° + 50°

⇒ x° = 180° – x°

Add x° on both sides of the equation, by addition property of equality.

⇒ x°  + x° = 180° – x° + x°

⇒ 2x° = 180°

Divide by 2 on both side of the equation, by division property of equality.

⇒ x° = 90°

Hence the value of x° is 90°.

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