Question

PLEASE HELP
In the same circle, chord AB determines a 115° arc and chord AC determines a 43° arc. Find m∠BAC.
(2 answers)

Answer 1

Answer:

101 or 36 degrees

Step-by-step explanation:

If you add up the measures of the arcs it is 158. That means BC is 202 degrees. Divide it by 2 to find the angle. For the second answer, remember the question did not specify if the arcs were major or minor so you can flip them around.

Answer 2

Answer:

m∠BAC is 101° or 36°.

Step-by-step explanation:

Given,

$m(\widehat{AB})=115^{\circ}$

$m(\widehat{AC})=43^{\circ}$

To find : The measurement of angle BAC,

Let O be the center of the circle.

Since, here we have to cases ( shown in diagram ),

In Case 1 :

$m\angle BOC = 360^{\circ}-[m(\widehat{AB})+m(\widehat{AC})]$

$=360^{\circ}-(115^{\circ}+43^{\circ})$

$=360^{\circ}-158^{\circ}$

$=202^{\circ}$

By the central angle theorem,

$m\angle BAC = \frac{m\angle BOC}{2}$

$=\frac{202^{\circ}}{2}=101^{\circ}$

In Case 2 :

$m\angle BOC = m(\widehat{AB})-m(\widehat{AC})$

$=115^{\circ}-43^{\circ}$

$=72^{\circ}$

Again by the central angle theorem,

$m\angle BAC = \frac{m\angle BOC}{2}$

$=\frac{72^{\circ}}{2}=36^{\circ}$