Question

Angle MON is a straight angle and bisects MOQ. What is the measure of MOP? 29° 58° 61° 122°

Answer 1

∠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 =
`(122)/(2)` = 61°

Answer 2

The measure of the angle MOP is 61° (Third option)

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°