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°.
