Question

List the sides of ΔFGH in order from least to greatest if m∠F = 5x + 6, m∠G = 12x - 4, and m∠H = 4x + 31.

Answer 1

F < G < H

Explanation:

Because a triangle's angles always add up to 180 degrees, you can add all the angle sides together to solve for x.

5x+6+12x-4+4x+31=180

21x=147

x=7

Now that you know that x=7, you can plug in 7 in each equation:

m∠F = 5(7)+6

m∠F = 41

m∠G = 12(7)-4

m∠G = 80

m∠H = 4(7)+31
m∠H = 59

Now that you have figured out each angle's sides, you also know that the side opposite of each angle determines it's size in relation to the other sides.

Because of this, you can order the side lengths by angle lengths, getting F < G < H.