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 $\text{m}\angle \text{AHD=}\mathbf{60}\mathbf{°}$. Find the measure of each angle.

$\mathit{\angle }\mathit{\text{FHG}}$.

Short answer

The angle$\angle \mathit{\text{FHG}}$ is $30°$.

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,

$\overleftrightarrow{AB}$bisects $\angle DHF$

$\angle AHD=\angle AHF=60°$

$\angle AHG=\angle AHF+\angle FHG$

role="math" localid="1649221456166" $90°=60°+\angle FHG$

$\angle FHG=30°$

Hence the angle $\angle FHG=30°$.

Step 3. State the conclusion.

Therefore, $\angle FHG=30°$.