Answer:
m∠EFG = [tex]161\°[/tex]
m∠LMN = [tex]19\°[/tex]
Step-by-step explanation:
Given:
∠EFG and ∠LMN are supplementary angles
m∠EFG = [tex](3x + 17)\°[/tex]
m∠LMN = [tex](\frac{1}{2}x - 5)\°[/tex]
We need to find m∠EFG and m∠LMN
Now we know that sum of the Supplementary angles are 180°
Hence we can say that;
m∠EFG + m∠LMN = 180°
Substituting the given values we get;
[tex](3x + 17)+ (\frac{1}{2}x - 5) = 180\\\\3x+17+\frac{1}{2}x-5 =180\\\\3x+\frac{1}{2}x-12=180\\\\3x+\frac{1}{2}x=180-12\\\\\frac{3x\times2}{2}+\frac{1}{2}x = 168\\\\\frac{6x+x}{2} = 168\\\\7x = 168\times2\\\\7x = 336\\\\x=\frac{336}{7}= 48[/tex]
Now Substituting the value of x to find the measures of angle;
m∠EFG = [tex](3x + 17)\° = (3\times48+17)\°= (144+17)\° =161\°[/tex]
m∠LMN = [tex](\frac{1}{2}x - 5)\°=(\frac{1}{2}\times 48 - 5)\°= (24 - 5)\°=19\°[/tex]
