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In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?

In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value-example-1
User Usmanali
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1 Answer

2 votes

Answer:

60°

Explanation:

In a circumscribed quadrilateral, opposite angles are supplementary.

x° = 180° -120°

x° = 60°

_____

Derivation of the relationship

Arcs BAD and BCD have a sum of 360°. Arc BAD is twice the measure of angle BCD. Likewise, arc BCD is twice the measure of angle BAD. So, we have ...

2∠BCD +2∠BAD = 360°

∠BCD +∠BAD = 180° . . . . . . divide by 2. This is the relation we used above.

User Shanoor
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