Question

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

$\angle \text{GHB}$

Short answer

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

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,

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

Two perpendicular lines make an angle of $90°$.

Hence the angle$\angle GHB=90°$.

Step 3. State the conclusion.

Therefore, $\angle GHB=90°$.