The measure of the angle MOP is 61° (Third option)
What is an angle?
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Angle MON is a straight angle → ∠MON=180°
∠QON=58° (according to the graph)
OP bisects angle ∠MOQ, then OP divides angle ∠MOQ into two equal angles:
∠MOP=∠POQ=∠MOQ/2 (1)
∠MOQ+∠QON=∠MON
Replacing the known values in the equation above:
∠MOQ+58°=180°
Solving for ∠MOQ: Subtracting 58° on both sides of the equation
∠MOQ+58°-58°=180°-58°
∠MOQ=122°
Replacing ∠MOQ by 122° in the equation (1)
(1) ∠MOP=∠POQ=122°/2
∠MOP=∠POQ=61°
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