Question

determining central and inscribed angles in circles
the ( mangle req ) is ( ) degrees
reason:
tools done

Explanation:

Step1: Recall the central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, the inscribed angle $\angle RCQ$ subtends arc $RQ$, and the central angle $\angle REQ$ also subtends arc $RQ$.

Step2: Calculate the measure of $\angle REQ$

Given that the inscribed angle $\angle RCQ = 53.3^{\circ}$. Using the formula $m\angle REQ=2\times m\angle RCQ$ (since the central angle is twice the inscribed angle subtending the same arc).
So, $m\angle REQ = 2\times53.3^{\circ}=106.6^{\circ}$

Answer:

$106.6$; Reason: The measure of a central angle is twice the measure of an inscribed angle subtending the same arc.