Answer:
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 = [tex]\frac{1}{2}[/tex] 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°
