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In the diagram QP and MP are straight lines. ∠NMR = 38° and ∠MPR = 44°. Find ∠QMP

June 4, 2026Mathematics

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Here are the solutions to the geometry problems.

Question 6:
In the diagram, Q, M, R, P are points on the circle. There is a tangent at point P.
Given:
$\angle NMR = 38^\circ$
$\angle MPR = 44^\circ$ (This is the angle between the tangent at P and the chord PR).

Apply the Alternate Segment Theorem.
The angle between the tangent at P and the chord PR ( $\angle MPR$ ) is equal to the angle subtended by the chord PR in the alternate segment ( $\angle PQR$ ).
So, $\angle PQR = \angle MPR = 44^\circ$ .
Use the property of angles subtended by the same arc