Question

In the diagram $\overleftrightarrow{\mathit{\text{AB}}}$bisects $\mathit{\angle }\mathit{\text{DHF}}$, $\overleftrightarrow{\mathit{\text{AB}}}\mathit{\perp }\overline{\mathit{\text{GH}}}$, $\overleftrightarrow{\mathit{\text{AB}}}\mathit{\parallel }\overleftrightarrow{\mathit{\text{CD}}}$, and $\mathit{\text{m}}\mathit{\angle }\mathit{\text{AHB=}}\mathit{60}\mathit{°}$. Find the measure of each angle.

$\mathit{\angle }\mathit{\text{DHC}}$

Short answer

The angle $\angle DHC$ is $60°$.

Step-by-step solution

Step 1. Observe the diagram.

Here, $\angle AHD=60°$, $\overleftrightarrow{AB}\perp \overline{GH}$, $\overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$ and $\overleftrightarrow{AB}$ bisects $\angle DHF$ .

Step 2. Show the calculation.

From the figure and the data,

$\angle AHF=\angle AHD=60°$. Since, $\overleftrightarrow{AB}$bisects $\angle DHF$.

$\begin{array}{c}\angle DHC=180-\angle AHF-\angle AHD\\ =180-60-60\\ =60\end{array}$

Hence the angle $\angle DHC=60°$.

Step 3. State the conclusion.

Therefore, $\angle DHC=60°$.