Answer:
m∠A = 42°
Step-by-step explanation:
* Lets revise some facts in the circle
- If the vertex of an angle on the circle and the two sides of the
angle are chords in the circle, then this angle is called
an inscribed angle
- Each inscribed angle subtended by the opposite arc, the arc name
is the starting point and the ending point of the angle
# Ex: ∠CAB is subtended by arc CB
- There is a relation between the inscribed angle and its
subtended arc, the measure of the inscribed angle equals half
the measure of its subtended arc
* Now lets solve the problem
- ∠CAB is an inscribed angle subtended by arc CB
∴ m∠CAB = (1/2) measure of arc CB
∵ The measure of arc CB = 84°
∴ The measure of ∠A = 1/2 × 84° = 42°
* m∠A = 42°
