If angle 4 is 52.7 what are the measures of angles 1, 2 and 3?

Mathematics

1 answer:

Paraphin [41]3 years ago

4 0

I use math-a-way it answers questions like that

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75 POINTS!!! WILL MARK BRAINLIEST!!! Find the measure of angle LNM

Harlamova29_29 [7]

m∠LNM = 54°

Here is why:

In this photo there are two important angles with very important features, a central angle and an inscribed angle.

A central angle is an angle that is in the center of the circle, so angle P is a central angle. The arc that is associated with this angle is going to be the same measure as the central angle. I have labeled this in the photo below as blue.

An inscribed angle is an angle that lies on the circle, so angle N is an inscribed angle. The arc that is associated with this angle will be double the amount of the inscribed angle, or the angle is half of the measure of the arc. I have labeled this in the photo below as red.

Since we know that the central angle is 108°, with what we know about central angles we know that arc LM is going to be 108° as well.

We also know that an inscribed angle is half the amount of the arc so...

108 ÷ 2 = 54

m∠LNM = 54°