What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 120?

Mathematics

2 answers:

disa [49]3 years ago

6 0

Answer:

540

Step-by-step explanation:

Has good dai

IrinaVladis [17]3 years ago

4 0

The answer would be 180 because the sum of the exterior angles would equal 360 and 360 divided by 120 equals 3 so that means there are 3 sides. Next you find out how much the interior angle is worth by subtracting it from 180 because they're supplementary you would find that the interior angle is equal to 60 degrees then multiply 60 degrees by how many sides there are (3) which equals 180 degrees.

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Zigmanuir [339]

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<u>Step-by-step explanation:</u>

The small triangle MNO is similar to the big triangle LNP, which means their sides are proportional

$\text{Small}\triangle \quad \text{Big}\triangle \\\\\\\dfrac{MN}{ON}=\dfrac{LN}{PN}\\\\\\\dfrac{24}{y}=\dfrac{9+24}{6+y}\\\\\\24(6+y)=y(9+24)\\144+24y=33y\\\\144=9y\\\\\large\boxed{16=y}$