Answer:
The measure of angle BAC = 101°
Step-by-step explanation:
* Lets study the problem
- A circle with two chords
- The two cords have common start point A on the circle
- The chord AB subtended arc AB with measure 115°
- The chord AC subtended arc AC with measure 43°
- The measure of any circle is 360°
* These two cords divide the circumference of the circle into
three arcs, arc AB , arc AC and arc BC
∵ The measure of arc AB = 115°
∵ The measure of arc AC = 43°
∵ The measure of the circle is 360°
∴ The measure of arc BC = 360 - (115 + 43) = 360 - 158 = 202°
- In the circle, the angle whose vertex is on the circle is
called inscribed angle and subtended by the opposite arc,
its measure is half the measure of the subtended arc
∵ ∠BAC is an inscribed angle subtended by arc BC
∴ m∠BAC = 1/2 measure of arc BC
∵ The measure of arc BC = 202°
∴ m∠BAC = 202 ÷ 2 = 101°
