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Angle MON is a straight angle and Ray O P bisects AngleMOQ.

Four lines extend from point O. The space between lines O M and O P is an orange arc. The space between lines P O and P Q has an orange arc. The space between lines O Q and O N is 58 degrees.
What is the measure of AngleMOP?

29°
58°
61°
122°

Respuesta :

answer

°

61°

Step-by-step explanation:

varshamittal029

The measure of ∠MOP=61°.

What is a straight angel?

A straight angle is an angle which measures 180°.

So according to the question,

∠MON is a straight angle.

⇒m∠MON=180°

∠QON=58° (according to the figure)

OP bisects ∠MOQ,

then OP makes ∠MOQ into two equal angles i.e. ∠MOP and ∠POQ:

∠MOP=∠POQ=∠MOQ/2  -----equation-1

As OQ divides ∠MON into two angles ∠MOQ and ∠QON. So,

m∠MOQ+m∠QON=m∠MON

⇒m∠MOQ+58°=180°

⇒m∠MOQ=180°-58°

⇒m∠MOQ=122°

Replacing ∠MOQ by 122° in the equation-1

m∠MOP=m∠POQ=m∠MOQ/2=122°/2

⇒m∠MOP=m<POQ=61°

Therefore the measure of ∠MOP=61°.

Learn more about the straight angle

here: https://brainly.com/question/16560125

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