Question

if an angle is bisected to form two new 24.8° angles, what was the measure of the original angle?

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal - measure angles. So if the original angle is \( \angle A \) and it is bisected into two angles \( \angle B \) and \( \angle C \), then \( \angle A=\angle B+\angle C \) and \( \angle B = \angle C \).

Step2: Calculate the original angle

Given that each of the new angles is \( 24.8^{\circ} \). Since the original angle is the sum of the two equal - measure angles formed by bisecting it, we can calculate the original angle as \( 24.8^{\circ}+24.8^{\circ} \) or \( 2\times24.8^{\circ} \).

\( 2\times24.8^{\circ}=49.6^{\circ} \)

Answer:

\( 49.6 \)