Question

if the m<bac=76 degrees, what is the m<boc?
for a circle?

Answer 1

Question 1.

Let $A,B,C$ be points on a circle with center $O$. If $m\angle BAC=76$ degrees, what is $m\angle BOC$?

Solution. The angle $\angle BAC$ is inscribed in the circle, and $\angle BOC$ is the central angle that subtends the same arc as $\angle BAC$. Therefore, the measure of $\angle BOC$ is twice the measure of $\angle BAC$. Thus,

$m\angle BOC=2m\angle BAC=2\cdot 76^{\mathrm{o}}=152^{\mathrm{o}}.$

Answer: $m\angle BOC=152^{\mathrm{o}}$. $\square$