Question

in circle n with ( mangle mnp = 42^{circ} ), find the ( mangle mqp ).

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
In circle \(N\), \(\angle MQP\) is an inscribed angle and \(\angle MNP\) is a central angle. Both angles subtend the arc \(MP\).

Step2: Apply the formula

By the inscribed - angle theorem, \(m\angle MQP=\frac{1}{2}m\angle MNP\).
Given \(m\angle MNP = 42^{\circ}\), then \(m\angle MQP=\frac{1}{2}\times42^{\circ}\).

Answer:

\(21^{\circ}\)