Question

In ΔMNO, m∠M = 57° and m∠N = 75°. Which list has the sides of ΔMNO in order from shortest to longest?

Answer 1

Answer:  Choice B

MN, NO, OM

Refer to the diagram below

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Explanation:

M = 57 and N = 75 are the two given angles.

Angle O is the missing angle of the triangle.

Recall that for any triangle, the three inside angles always add to 180

M+N+O = 180

57+75+O = 180

132+O = 180

O = 180-132

O = 48

Angle O is 48 degrees.

Note: be sure not to mix up the letter 'oh' with the number zero. Unfortunately, they look very similar.

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We know the following three angles of this triangle

• M = 57
• N = 75
• O = 48

As a rule, the smallest side is always opposite the smallest angle. The smallest angle is O = 48, and the side opposite that is MN.

Also, the largest side is always opposite the largest angle. The largest angle is N = 75, and the side opposite that is OM

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In short, we found that MN is the smallest side and OM is the longest side.

That must mean side NO is placed in the middle of MN and OM

So that's how we get get the answer of MN, NO, OM which is choice B.

Refer to the diagram below.