Question

Math Help Part 5 (Please Help)

Answer 1

First find rest angles

• m<GJH=180-(76+63)=180-180-139=41
• mGJI=180-41=139°
• m<IGJ=180-(139+12)=189-151=29°

Now we know that smaller angle has smaller opposite side and vice versa.

So

The order is

• GH<HJ<GJ<IJ<GI

Answer 2

GH < HJ < GJ < JI < GI

Explanation:

In a triangle:

• The smallest side length is opposite the smallest angle
• The longest side length is opposite the largest angle

Also,

• The sum of the interior angles of a triangle is 180°

m∠G = 180 - 12 - 76 = 90°

m∠H = 76°

m∠I = 12°

⇒ GH < GI < HI

Triangle GHJ:

m∠HGJ = 63°

m∠GHJ = 76°

m∠GJH = 180 - 76 - 63 = 41°

⇒ GH < HJ < GJ

Triangle JGI

m∠JGI = 180 - 12 - 139 = 29°

m∠GIJ = 12°

m∠GJI = 180 - 41 = 139°

⇒ GJ < JI < GI

Final solution: GH < HJ < GJ < JI < GI