Question

Please help and show steps I have been trying to understand for two days now!!

AngleEFG and angle GFH are a linear pair. mangleEFG=5n+24 and mangleGFH=3n+12. What are mangle EFG and mangleGFH?

Answer 1

Answer:180

Step-by-step explanation: Well, since the two angles are a linear pair, they are supplementary or add up to 180 degrees.

measure of angle EFG + measure of angle GFH = 180

(33N + 1616) + (55N + 2828) = 180

combining like terms, 88N + 4444 = 180

Solving for N results in N = (180 - 4444)/88 = -4264/88 = -533/11 = -48 and 5/11 or -48.454545....

This improper fraction of -533/11 ironically turns out to be quite helpful.

Substituting this value into the expressions above produce the following angles.

Angle EFG = 33N+1616 = 33(-533/11)+1616 = 1616 - 33*533/11 <-- property/definition of subtraction

= 1616 - 3*533 <-- because 33 and 11 cancel out

= 1616 - 1599 <-- order of mixed operations; PEMDAS

Likewise, yep

Angle GFH = 55(-533/11)+2828 = 2828 - 55*533/11

= 2828 - 5*533 <-- becuase 55 and 11 cancel out

= 2828 - 2665

= 163

Notice that the sum of these angles are in fact 17 + 163 = 180

Answer 2

m∠EFG = 114°

m∠GFH = 66°

Explanation:

It is given in the question

m∠EFG = 5n + 24

and m∠GFH = 3n + 12

Since both the angles ∠EFG and ∠GFH are linear pair.

Therefore, m∠EFG + m∠GFH = 180°

Now we plug in the measures of the given angles

(5n + 24) + (3n + 12) = 180

(5n + 3n) + (24 + 12) = 180

8n + 36 = 180

8n = 180 - 36

8n = 144

`n=(144)/(8)`

n = 18

Since m∠EFG = 5n + 24

m∠EFG = 5×18 + 24

= 90 + 24

= 114°

m∠GFH = 3n + 12

= 3×18 + 12

= 54 + 12

= 66°