Question

select the correct answer from each drop - down menu. given that ∠bdc = 29°, ∠bac = ° and ∠boc = °

Explanation:

Step1: Recall inscribed - angle theorem

Angles in the same segment of a circle are equal. $\angle BDC$ and $\angle BAC$ are angles in the same segment of the circle with center $O$. So, $\angle BAC=\angle BDC$.
Since $\angle BDC = 29^{\circ}$, then $\angle BAC=29^{\circ}$.

Step2: Recall central - angle theorem

The central - angle is twice the inscribed - angle subtended by the same arc. $\angle BOC$ is the central - angle and $\angle BDC$ is the inscribed - angle subtended by the arc $BC$.
So, $\angle BOC = 2\angle BDC$.
Substitute $\angle BDC = 29^{\circ}$ into the formula: $\angle BOC=2\times29^{\circ}=58^{\circ}$.

Answer:

$\angle BAC = 29^{\circ}$, $\angle BOC = 58^{\circ}$