Question

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

$\angle GHB$

Short answer

The angle $\angle GHB$is${\mathbf{90}}^{\circ }$

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,

$\overleftrightarrow{AB}\perp \overline{GH}$

Two perpendicular lines make an angle of ${90}^{\circ }$.

Hence the angle$\angle GHB={90}^{\circ }$

Step 3. State the conclusion.

Therefore, $\angle GHB={90}^{\circ }$.