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

Answer:

m∠EFG = 114°

m∠GFH = 66°

Step-by-step 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

$n=\frac{144}{8}$

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°