Geometry

Question Analysis

The main focus is using the property that opposite angles in a cyclic quadrilateral are supplementary to find the value of . Then, use the inscribed - angle theorem to find the measure of arc .

 

Key Concept Explanation

1. Cyclic Quadrilateral Property: In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is . So, for cyclic quadrilateral , .

2. Inscribed - Angle Theorem: The measure of an inscribed angle is half of the measure of the arc it intercepts.

 

Step - by - Step Solution

1. Since is a cyclic quadrilateral, we set up the equation based on the cyclic - quadrilateral property:

.

Substitute and into the equation:

.

2. Combine like terms:

,

.

3. Solve for :

Add 60 to both sides of the equation:

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