Answer: [A]: " 78 ° " .
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Explanation:
Supplementary angles add up to 180 degrees.
So, given m∠F & m∠G are supplementary angles:
and given m∠F = (4x + 22) and: m∠G = (6x + 18) ;
Find m∠F ; which equals (4x + 22).
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So, add the 2 (two) supplementary angles;
set them as "equal to 180" ;
solve for x ;
then: plug that x value into:
(4x + 22) ; which is the m∠F ;
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4x + 22 + 6x + 18 = 180 ;
On the 'right-hand side of the equation" ;
"combine the like terms" :
+ 4x + 6x = + 10x ;
+ 22 + 18 = 40 ;
Then rewrite the equation:
10x + 40 = 180 ;
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Now:
Method 1):
Subtract 40 from Each Side of the equation:
10x + 40 − 40 = 180 − 40 ;
to get: 10x = 140 ;
Now: Divide Each Side of the equation by 10 ; to isolate x on one side of the equation; & to solve for x ;
10x / 10 = 140 / 10 ; to get: " x = 14 " ;
Method 2):
When we have: 10x + 40 = 180 ;
Divide the entire equation (i.e. Each Side of the equation) by 10 ;
to get rid of the "zeros" :
(10x + 40) / 10 = (180)/10 ;
to get:
(10x/10) + (40/10) = (180/10);
→ x + 4 = 18 ;
Subtract 4 from Each Side of the equation; to isolate x on one side of the equation; & to solve for x ;
x + 4 − 4 = 18 − 4 ;
to get: x = 14 .
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Now, find m∠F = 4x + 22 ;
Plug in 14 for x ; to solve:
m∠F = 4(14) +22 ;
= 56 + 22 ;
m∠F = 78°
which corresponds to:
Answer choice: [A]: 78° .
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Hope this is helpful to you!
Wishing you well!
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