Question

Item Prompt

Segment MP is a diameter of circle O.
150°
What is the measure of arc MN?
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Answer 1

30°

Explanation:

Segment MP is the diameter of the circle, hence angle MOP has the measure of 180°.

Angles MON and NOP are supplementary angles (add up to 180°). Thus,

m∠MON+m∠NOP=180°

m∠MON=180°-m∠NOP

m∠MON=180°-150°=30°.

Angle MON is the central angle subtended on the arc MN. Thus, the measure of the arc MN is 30°.

Answer 2

Arc MN is 30°

Explanation:

It's important to know that the whole arc of a circle is 360°.

So, if MP is a diameter, that means it divides the circle in two equal parts of 180° each.

Now, one half of this arc is formed by MN and 150°, so we can formulate the expression

`MN+150\° = 180\° \\MN= 30\°`

Therefore, the arc MN is 30°.