Question

question 12: standard g.c.2
geometry
if inscribed angle cdb is 22 degrees, what is the measure of arc cb?
circle with points d, c, b and center a

a. 22
b. 11
c. 44
d. 88

Explanation:

Step1: Recall Inscribed Angle Theorem

The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. So, if \(\angle CDB\) is an inscribed angle intercepting arc \(CB\), then \(m\angle CDB=\frac{1}{2}m\overset{\frown}{CB}\).

Step2: Solve for Arc \(CB\)

Given \(m\angle CDB = 22^\circ\), substitute into the formula:
\(22^\circ=\frac{1}{2}m\overset{\frown}{CB}\)
Multiply both sides by 2:
\(m\overset{\frown}{CB}=2\times22^\circ = 44^\circ\)

Answer:

c. 44