Question

find the measure of the arc.

m\\(widehat{fd}\\) = ?°

Explanation:

Step1: Recall arc - angle relationship

The measure of an arc is equal to the measure of its central angle.

Step2: Calculate central angle for arc $\widehat{FD}$

The central angle for arc $\widehat{FD}$ can be found by subtracting the right - angle ($90^{\circ}$) and the given angle ($146^{\circ}$) from $360^{\circ}$. First, find the sum of the known angles: $90 + 146=236^{\circ}$. Then, $m\angle FOD=360 - 236$.
$m\angle FOD = 124^{\circ}$
Since the measure of an arc is equal to the measure of its central angle, $m\widehat{FD}=124^{\circ}$

Answer:

$124$