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 role="math" localid="1647713022816" $\mathit{\text{m}}\mathit{\angle }\mathit{\text{AHB=}}60°$. Find the measure of each angle.

$\mathit{\angle }\mathit{\text{HCD}}$

Short answer

The angle$\mathit{\angle }\mathit{\text{HCD}}$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,

$\angle BHC$and $\angle AHF$are vertical angles and they are congruent.

$\angle BHC=\angle AHF=60°$

$\angle BHC$and $\angle AHF$are alternate angles and they are congruent.

$\angle BHC=\angle HCD=60°$

Hence the angle $\angle HCD=60°$.

Step 3. State the conclusion.

Therefore, $\angle HCD=60°$.