Question

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Answer 1

See below ~

Explanation:

Q9

• x = 200° (arc measure = central angle measure)
• The inscribed angle y is half of the arc length x
• y = 1/2x
• y = 1/2(200°)
• y = 100°

Q10

• x + 112 = 180
• x = 68°
• y + 81 = 180
• y = 99°

Answer 2

9. x = 200 and y = 100

10. x = 68 and y = 99

Explanation:

Question 9

The measure of an arc is the measure of its central angle.

⇒ x = 200

This is a non-cyclic quadrilateral as not all its vertices touch the circumference of the circle.

The angle at the center is twice the angle at the circumference.

⇒ y = 200 ÷ 2

⇒ y = 100

Question 10

This is a cyclic quadrilateral as all its vertices touch the circumference of the circle.

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

⇒ x + 112 = 180

⇒ x = 68

⇒ y + 81 = 180

⇒ y = 99