Question

∠EFG and ∠GFH are a linear​ pair, m∠EFG 3n+17​, and m∠GFH 5n+27. What are m∠EFG and m∠​GFH?

Please help asap.

Answer 1

Answers:

• m∠EFG = 68 degrees
• m∠​GFH = 112 degrees

=============================================================

Step-by-step explanation:

As the name suggests, "linear pair" means the angles form a straight line when glued together. Therefore, the angle measures add to 180 degrees. We consider them supplementary angles.

So,

(angle EFG) + (angle GFH) = 180

(3n+17) + (5n+27) = 180

(3n+5n) + (17+27) = 180

8n+44 = 180

8n = 180-44

8n = 136

n = 136/8

n = 17

Then we can find each angle

• angle EFG = 3n+17 = 3*17+17 = 51 + 17 = 68
• angle GFH = 5n+27 = 5*17+27 = 85+27 = 112

In short,

• angle EFG = 68 degrees
• angle GFH = 112 degrees

Adding those angles gets us 68+112 = 180 to confirm we have the correct answers.

Answer 2

∠EFG = 68°

∠GFH = 112°

Step-by-step explanation:

Linear pair: Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

Therefore, if ∠EFG and ∠GFH are a linear pair, their sum is 180°.

⇒ ∠EFG + ∠GFH = 180°

⇒ (3n + 17) + (5n + 27) = 180

⇒ 3n + 17 + 5n + 27 = 180

⇒ 3n + 5n + 17 + 27 = 180

⇒ 8n + 44 = 180

⇒ 8n + 44 - 44 = 180 - 44

⇒ 8n = 136

⇒ 8n ÷ 8 = 136 ÷ 8

⇒ n = 17

To find the measures of ∠EFG and ∠GFH, substitute the found value of n into the expression for each angle:

⇒ ∠EFG = 3(17) + 17 = 68°

⇒ ∠GFH = 5(17) + 27 = 112°

Check by adding them together:

⇒ ∠EFG + ∠GFH = 68° + 112° = 180°

This confirms that the two angles are a linear pair.