Angle EFG and angle GFH are a linear pair, m<EFG=2n+21,and m<GFH=4n+15. What are m<EFG and m<GFH?
since they are a linear pair,
2n+21 + 4n+15 = 180
solve for n, and then you can find the measures.
Given that angle EFG and angle GFH are a linear pair, the sum of their measures is 180 degrees.
We are also given that m<EFG = 2n + 21 and m<GFH = 4n + 15.
Since the sum of their measures is 180 degrees, we can set up an equation:
(2n + 21) + (4n + 15) = 180
Simplifying the equation:
6n + 36 = 180
Subtracting 36 from both sides:
6n = 144
Dividing by 6:
n = 24
Now we can find the measures of the angles:
m<EFG = 2n + 21 = 2(24) + 21 = 48 + 21 = 69 degrees
m<GFH = 4n + 15 = 4(24) + 15 = 96 + 15 = 111 degrees
Therefore, m<EFG = 69 degrees and m<GFH = 111 degrees.
To find the measures of angles EFG and GFH, we need to solve for the variables in the given equations.
Given:
m<EFG = 2n + 21
m<GFH = 4n + 15
Since angle EFG and angle GFH form a linear pair, their measures should add up to 180 degrees.
Therefore, we can set up an equation:
m<EFG + m<GFH = 180
Substituting the given values:
(2n + 21) + (4n + 15) = 180
Now, we can simplify the equation:
6n + 36 = 180
Subtracting 36 from both sides:
6n = 144
Dividing both sides by 6:
n = 24
Now, we can substitute the value of n back into the equations to find the measures of angles EFG and GFH:
m<EFG = 2n + 21
m<EFG = 2(24) + 21
m<EFG = 48 + 21
m<EFG = 69 degrees
m<GFH = 4n + 15
m<GFH = 4(24) + 15
m<GFH = 96 + 15
m<GFH = 111 degrees
Therefore, the measure of angle EFG is 69 degrees, and the measure of angle GFH is 111 degrees.