Question

Could someone please help with 15 and 16

Answer 1

15.

Since m∠FHI = 142, make m∠FHG and m∠GHI add up to 142 in an equation.

(3x + 6) + (9x - 8) = 142

• Combine like terms.

12x - 2 = 142

• Add 2 to both sides.

12x = 144

• Divide both sides by 12.

x = 12

• Plug 12 for x in m∠FHG and m∠GHI.

m∠FHG = 3(12) + 6 = 42

m∠GHI = 9(12) - 8 = 100

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16.

Since ∠JKL is a right angle, it must be 90 degrees. Make m∠JKM and m∠MKL add up to 90 in equation.

(12x + 3) + (6x - 3) = 90

• Combine like terms.

18x = 90

• Divide both sides by 18.

x = 5

• Plug 5 for x into m∠JKM and m∠MKL.

m∠JKM = 12(5) + 3 = 63

m∠MKL = 6(5) - 3 = 27

Answer 2

let's do 15 first.

From the model, we can conclude that 3x + 6 + 9x - 8 = 142. We then solve:

12x - 2 = 142 => 12x = 144 => x = 12

Then we complete the equations and solve to get:

3x + 6 = 42 and 9x - 8 = 100

Now number 16.

We can conclude from the model that 12x + 3 + 6x - 3 = 90. We solve to get:

18x = 90 => x = 5

Then we complete the equations and get:

12x + 3 = 63 and 6x - 3 = 27

So, for 15, 3x + 6 = 42 and 9x - 8 = 100. For 16, 12x + 3 = 63 and 6x - 3 = 27.

Hope this helps!