2.
AB is a diameter of a circle, center O.
C is a point on the circumference of the circle, such that What is the size of CBA?

A.30
B.40
C.45
D.60

The size of ∠CBA is 30° ⇒ A

Step-by-step explanation:

The measure of an inscribed angle subtended by semi-circle is 90°, because the measure of the inscribed angle is one-half the measure of the subtended arc and the measure of the semi-circle is 180°, then one-half 180° is 90°

In circle O

∵ C lies on the circumference of the circle

∴ ∠ACB is an inscribed angle

∵ ∠ACB subtended by arc AB

∴ m∠ACB = m of arc AB

∵ AB is the diameter of the circle

- That means arc AB is a semi-circle

∵ m arc AB = 180°

∴ m∠ACB = 90°

In Δ ACB

∵ m∠CAB + m∠CBA + m∠ACB = 180° ⇒ interior angles of Δ

∵ m∠CAB = 2 m∠CBA

- Substitute m∠ACB by 90 and m∠CAB by 2 m∠CBA

∴ 2 m∠CBA + m∠CBA + 90 = 180

∴ 3 m∠CBA + 90 = 180

- Subtract 90 from both sides

∴ 3 m∠CBA = 90

- Divide both sides by 3

∴ m∠CBA = 30°

The size of ∠CBA is 30°

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step-by-step explanation:

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