In the same circle, chord ab determines a 115° arc and chord
ac determines a 43° arc. find m∠bac.

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°

true

step-by-step explanation:

step-by-step explanation:

b and c