Question

What is the measure of DG? Enter your answer in the box.

Answer 1

For a better understanding of the explanation provided here please find the accompanying diagram in the file that has been attached. In the diagram, O is the center of the circle and $\angle DOG$ subtends the same arc DG as $\angle DHG$.

To find the measure of the arc DG, or $\overarc{DG}$, we will have to use the Inscribed Angle Theorem which states that "The measure of an inscribed angle is equal to one-half the measure of its intercepted arc".

Now, we know that the inscribed angle given is $\angle DHG=55^0$. As per the theorem this is half of the measure of the intercepted arc which is $\angle DOG$.

Therefore, $\angle DOG=2\angle DHG=2\times 55^{\circ}=110^{\circ}$

Thus, the measure of DG, or $\overarc{DG} =110^{\circ}$ is the correct answer.

Answer 2

The answer is 110. I just took the quiz on k12