The value of the angle ∠ MNQ will be 40°. The correct option is D.
What is the angle of chords theorem?
When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The inscribed angle MNQ is half the measure of its intercepted arc, so
∠ MNQ = ( 1 / 2 )MQ
∠ MNQ = 0.5 × 80°
∠ MNQ = 40°
Therefore, the value of the angle ∠ MNQ will be 40°. The correct option is D.
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