∠MOP = 61°
∠MOQ + ∠QON = 180° ( angles on a straight angle )
∠QON = 58° ( given )
∠MOQ = 180° - 58 = 122° ( difference of angles on straight angle )
∠MOP = ∠POQ ( MON is angle bisector )
∠MOP = [tex]\frac{122}{2}[/tex] = 61°
Answer:
The measure of the angle MOP is 61° (Third option)
Step-by-step explanation:
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° 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°
