<EFG and <GFH are a linear pair. m<EFG=5n+24 and m<GFH=3n+12. What are m<angle EFG and m<GFH?
a linear pair sums to 180ยบ
5n + 24 + 3n + 12 = 180
solve for n , then substitute back to find the angles
To find the measures of angles <EFG and <GFH, we can use the given information that <EFG and <GFH form a linear pair. A linear pair is a pair of adjacent angles whose measures add up to 180 degrees.
Let's start by setting up an equation using the given information:
m<EFG + m<GFH = 180
Substitute the expressions for each angle's measure into the equation:
(5n + 24) + (3n + 12) = 180
Combine like terms:
8n + 36 = 180
Now, we can solve for n:
8n = 180 - 36
8n = 144
n = 144 / 8
n = 18
Now that we have found the value of n, we can substitute it back into the expressions for the angle measures:
m<EFG = 5n + 24 = 5(18) + 24 = 90 + 24 = 114 degrees
m<GFH = 3n + 12 = 3(18) + 12 = 54 + 12 = 66 degrees
Therefore, the measure of <EFG is 114 degrees, and the measure of <GFH is 66 degrees.