Question

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

Answer 1

60°

Explanation:

In a circumscribed quadrilateral, opposite angles are supplementary.

x° = 180° -120°

x° = 60°

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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.