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

can someone help me here (show the solution)​

Find the value of x and/or y in OA. can someone help me here (show the solution)​-example-1

2 Answers

11 votes

Answer:

∠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
User Blackraspberryyy
by
7.4k points
8 votes

Answer:

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°

User Riyaz
by
7.8k points

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