Question

Find the m/_I, and write the sides in order from shortest to longest

Answer 1

m< I = 39°; GH, HI, GI

Explanation:

To find the measure of angle I, you can subtract 58 and 83 from 180, since the sum of the interior angles in a triangle is 180 degrees:

180 - 58 - 83 = 39

Then, to order the side lengths of triangle GHI from least to greatest, you can use the triangle theorem that the longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Therefore, since angle I is the smallest angle, side GH is the shortest side since they are opposite from one another. Similarly, since angle H is the largest angle, side GI is the largest side since they are opposite from one another.

You can now order the sides from smallest to largest, knowing the angle measures in triangle GHI:

GH is the smallest side, HI is larger than GH but smaller than GI, and GI is the largest side.

Therefore, the final answer is m< I = 39°; GH, HI, GI.

I hope this helps!