Question

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

$\angle \text{BHC}$.

Short answer

The angle$\angle \text{BHC}$ is ${\mathbf{60}}^{\circ }$.

Step-by-step solution

Step 1. Observe the diagram.

Here, $\angle AHD={60}^{\circ }$, $\overleftrightarrow{AB}\perp \overline{GH}$, $\overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$ 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.

$\angle AHF=\angle AHD={60}^{\circ }$

Since, $\overleftrightarrow{AB}$bisects $\angle DHF$.

Hence the angle $\angle BHC={60}^{\circ }$.

Step 3. State the conclusion.

Therefore, $\angle BHC={60}^{\circ }$.