Question

the drop down menu is the same on both sides

Answer 1

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

$\begin{gathered} \measuredangle BDC=\frac{1}{2}BC \\ \\ 29=\frac{1}{2}BC \\ \\ 2(29)=BC \\ \\ 58=BC \end{gathered}$

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