Final answer:
The measure of angle BAC is 22°.
The measure of angle BAC in triangle ABC inscribed in circle D can be found by doubling the measure of angle CBD and then halving it due to the Inscribed Angle Theorem. Angle BAC measures 44 degrees.
Step-by-step explanation:
The measure of angle BAC can be found using the fact that the angle inscribed in a circle is half the measure of the intercepted arc.
Since m angle CBD = 44°, the intercepted arc m arc CD is also 44°.
Therefore, the measure of angle BAC is half the measure of arc CD, which is 22°.
To find the measure of angle BAC in △ABC inscribed in circle D, we use the Inscribed Angle Theorem. This theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Given that m ∠ CBD = 44°, and CBD intercepts the same arc as angle BAC, angle BAC must be half of this measure.
Steps to Find m ∠ BAC
Identify the intercepted arc for angle CBD, which is also intercepted by angle BAC.
Double the measure of m ∠ CBD to find the measure of the intercepted arc.
Divide the measure of the intercepted arc by 2 to find the measure of angle BAC.
Following these steps:
Since m ∠ CBD = 44°, the intercepted arc measures 88°.
Therefore, m ∠ BAC = 44° because it is half of the intercepted arc's measure.