angle EFG and angle GFH are a linear pair, m angle EFG = 4n + 16, and m angle GFH = 5n + 38. What are m angle EFG and m angle GFH?
Angles that form a linear pair add up to 180 degrees. Therefore, we can set up the following equation:
4n + 16 + 5n + 38 = 180
Combine like terms:
9n + 54 = 180
Subtract 54 from both sides:
9n = 126
Divide both sides by 9:
n = 14
Now, plug n = 14 back into the original equations to find the measures of the angles.
m angle EFG = 4n + 16 = 4(14) + 16 = 56 + 16 = 72
m angle GFH = 5n + 38 = 5(14) + 38 = 70 + 38 = 108
So, m angle EFG = 72 degrees and m angle GFH = 108 degrees.
We are given that angles EFG and GFH are a linear pair. In a linear pair, the angles are supplementary, which means they add up to 180 degrees.
Let's solve for the measures of angles EFG and GFH:
m angle EFG + m angle GFH = 180
4n + 16 + 5n + 38 = 180
9n + 54 = 180
9n = 180 - 54
9n = 126
To solve for n, we divide both sides of the equation by 9:
n = 126 / 9
n = 14
Now, we can find the measures of angles EFG and GFH by substituting the value of n:
m angle EFG = 4n + 16
m angle EFG = 4(14) + 16
m angle EFG = 56 + 16
m angle EFG = 72
m angle GFH = 5n + 38
m angle GFH = 5(14) + 38
m angle GFH = 70 + 38
m angle GFH = 108
Therefore, m angle EFG = 72 degrees and m angle GFH = 108 degrees.
To find the measures of angles EFG and GFH, we need to set up an equation based on the fact that they are a linear pair.
A linear pair of angles is formed when two angles are adjacent (share a common vertex and side) and their non-common sides form a straight line. In a linear pair, the sum of the angle measures is always equal to 180 degrees.
So, we have the equation:
m(angle EFG) + m(angle GFH) = 180
Now, we can substitute the given expressions for the measures of angles EFG and GFH into the equation:
4n + 16 + 5n + 38 = 180
Combining like terms:
9n + 54 = 180
Subtracting 54 from both sides:
9n = 126
Dividing both sides by 9:
n = 14
Now that we have the value of n, we can substitute it back into the expressions for the measures of angles EFG and GFH to find their specific values.
m(angle EFG) = 4n + 16 = 4(14) + 16 = 56 + 16 = 72 degrees
m(angle GFH) = 5n + 38 = 5(14) + 38 = 70 + 38 = 108 degrees
Therefore, the measure of angle EFG is 72 degrees and the measure of angle GFH is 108 degrees.