Answer:
∡BCA = 29
∡BOC = 58
Explanation:
The angles BDC and BAC form the same arc on the circle, the arc BC. Then, these angles have the same measure, so
∡BCA = ∡BDC
∡BCA = 29
Then, we can use the inscribed angle theorem to find the arc BC as follows
[tex]\begin{gathered} \measuredangle BDC=\frac{1}{2}BC \\ \\ 29=\frac{1}{2}BC \\ \\ 2(29)=BC \\ \\ 58=BC \end{gathered}[/tex]
Therefore, arc BC has a measure of 58 degrees, which means that ∡BOC is equal to
∡BOC = Arc BC
∡BOC = 58
So, the answers are
∡BCA = 29
∡BOC = 58
