Question 24

In the adjoining figure, $$ABCDEFGH$$ is a regular octagon. The measure of $$\angle ADG$$ in degrees is ______.

Correct Answer: 45

Solution

The vertices of a regular octagon lie on a circle, and each central angle is $$\frac{360^\circ}{8}=45^\circ$$. The minor arc from $$A$$ to $$G$$ through $$H$$ spans two sides, so its measure is $$90^\circ$$. The inscribed angle $$\angle ADG$$ subtending this arc is half of $$90^\circ$$, which is $$45^\circ$$.

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