Question

cp geometry name: ____________ 1.04 quiz date: __________ hour: ____________ use the figure to answer questions #1 - 4 1) name an angle that is complementary to ∠dhc. 2) name an angle that is supplementary to ∠dhc. 3) name an angle that is vertical to ∠dhc. 4) name an angle that is adjacent to ∠dhc.

Explanation:

Step1: Recall complementary angles definition

Complementary angles add up to 90 degrees. Since $\angle BHD = 90^{\circ}$, and $\angle BHC+\angle CHD=90^{\circ}$, an angle complementary to $\angle DHC$ is $\angle BHC$.

Step2: Recall supplementary angles definition

Supplementary angles add up to 180 degrees. $\angle AHC$ and $\angle DHC$ form a linear - pair (a straight - line $\angle AHD = 180^{\circ}$), so an angle supplementary to $\angle DHC$ is $\angle AHC$.

Step3: Recall vertical angles definition

Vertical angles are formed by two intersecting lines and are opposite each other. There are no two - line intersections that form $\angle DHC$ in a way to have a vertical angle in the given figure. If we assume the lines are extended, there is no such angle shown. But if we consider the intersection of the lines that form $\angle DHC$, a non - existent in - figure but conceptually vertical angle would be non - applicable here as the figure doesn't show the proper intersection setup. However, if we consider the general concept, we can say there is no vertical angle shown in the figure for $\angle DHC$.

Step4: Recall adjacent angles definition

Adjacent angles share a common side and a common vertex. An angle adjacent to $\angle DHC$ is $\angle CHE$.

Answer:

1. $\angle BHC$
2. $\angle AHC$
3. No vertical angle shown in the figure
4. $\angle CHE$