Question

which of the following is an acute angle drawn in the figure below? ∠fgc ∠fgd ∠gba ∠abd

Explanation:

Step1: Recall acute - angle definition

An acute angle is an angle whose measure is between 0° and 90°.

Step2: Analyze each option

• $\angle FGC$: There is a right - angle symbol at $\angle FGC$, so $\angle FGC = 90^{\circ}$, not acute.
• $\angle FGD$: $\angle FGD$ and $\angle FGC$ are supplementary (linear pair). Since $\angle FGC=90^{\circ}$, $\angle FGD = 90^{\circ}$, not acute.
• $\angle GBA$: $\angle GBA$ and the right - angle $\angle FGC$ are vertical angles. Vertical angles are equal, so $\angle GBA = 90^{\circ}$, not acute.
• $\angle ABD$: $\angle ABD$ and $\angle GBA$ are supplementary (linear pair). Since $\angle GBA = 90^{\circ}$, $\angle ABD$ is an acute angle as it is less than 90°.

Answer:

$\angle ABD$