Answer:
2) m∠CBD = 25°
The measure of arc CDB = 230°
4) m arc XY = 10°
The measure of arc WZX = 330°
6) The answer is (c) ⇒ 10 millimeters
Step-by-step explanation:
2) ∵ the measure of arc BC = 130°
∵ Arc BCD is the semi-circle its measure 180°
∴ The measure of arc cd = 180 - 130 = 50°
∵ ∠CBD is inscribed angle subtended by arc CD
∴ m∠CBD = 1/2 measure arc CD
∴ m∠CBD = 50 ÷ 2 = 25°
∵ The measure of the circle is 360°
∵ The measure of arc BC = 130°
∴ The measure of arc CDB = 360 - 130 = 230°
4) ∵ The measure of arc WY = 40°
∵ The measure of arc XZ = 30°
∵ The measure of arc WZ = 60°
∵ m arc WY + m arc XZ - m arc XY = m arc WZ
∴ m arc XY = 40 + 30 - 60
∴ m arc XY = 10°
∵ The measure of the circle is 360°
∴ The measure of arc WZX = 360 - m arc WX
∵ The measure of arc WX = WY - XY = 40 - 10 = 30°
∴ The measure of arc WZX = 360 - 30 = 330°
6) In the circle O
∵ OC ⊥ AB and OX ⊥ ZY
∵ OC = OX
∴ AB = ZY ⇒ Theorem
∵ AB = 10 millimeters
∴ ZY = 10 millimeters ⇒ answer (C)
