Question

Find the value of x
and/or y in OA.

can someone help me here (show the solution)​

Answer 1

∠x = 93°

∠y = 97°

Explanation:

Finding x :

• x is an inscribed angle
• Its value is half of the arc opposing it
• x = (64 + 122) / 2
• x = 186/2
• x = 93

Finding y :

• The figure shows a cyclic quadrilateral circumscribed by a circle
• Hence, opposing angles are supplementary (add up to 180)
• y + 83 = 180
• y = 97

Answer 2

x = 93°

y = 97°

Explanation:

Angle y

A cyclic quadrilateral is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.

The opposite angles in a cyclic quadrilateral add up to 180°

⇒ y = 180° - 83°

⇒ y = 97°

Angle x

Inscribed Angle Theorem: the measure of an inscribed angle is half the measure of its intercepted arc.

Inscribed angle: an angle with its vertex on the circle and whose sides are chords.

Intercepted arc: the arc that is inside the inscribed angle and whose endpoints are on the angle.

x is an inscribed angle and (122° + 64°) is its intercepted arc.

⇒ x = (122° + 64°) ÷ 2

⇒ x = 93°