## Elementary Geometry for College Students (7th Edition)

$m\angle EHG=93^{\circ}$
We are given that the $m\angle EOG=82^{\circ}$. Radii $\overline{OE}=\overline{OG}$, creating an isosceles triangle. The sum of the interior angles of a triangle is $180^{\circ}$. Subtracting the vertex angle, and dividing the result by two will give us the measure of the base angles...more importantly, the $m\angle E$. $180-82=98\div2=49$ $m\angle E=49^{\circ}$ We learned from part d that the $m\angle DGE=38^{\circ}$. Using the sum of the interior angles for $\triangle GEH$... $180-49-38=93$ $m\angle EHG=93^{\circ}$