One angle is 10 degrees more than 4 times the other. Find the measure of each angle if
a) they are complimentary, and
b) they are supplementary
one angle ---- x
other angle -- 4x+10
a) x + 4x+10 = 90
b) x + 4x+10 = 180
in each case , solve for x
To solve this problem, we'll need to set up equations based on the given information and then solve for the angles.
a) Complementary angles have a sum of 90 degrees.
Let's define the two angles as x and y.
From the given information, we know that one angle is 10 degrees more than 4 times the other. So we can set up the equation:
x = 4y + 10
Since the angles are complementary, their sum is 90 degrees:
x + y = 90
Now we can substitute the value of x from the first equation into the second equation:
(4y + 10) + y = 90
5y + 10 = 90
5y = 90 - 10
5y = 80
y = 80/5
y = 16
Now we can substitute the value of y back into the first equation to find x:
x = 4y + 10
x = 4(16) + 10
x = 64 + 10
x = 74
So, the two angles are 74 degrees and 16 degrees.
b) Supplementary angles have a sum of 180 degrees.
Using the same variables, x and y, we can set up the equation based on the given information:
x = 4y + 10
Since the angles are supplementary, their sum is 180 degrees:
x + y = 180
Now we can substitute the value of x from the first equation into the second equation:
(4y + 10) + y = 180
5y + 10 = 180
5y = 180 - 10
5y = 170
y = 170/5
y = 34
Now we can substitute the value of y back into the first equation to find x:
x = 4y + 10
x = 4(34) + 10
x = 136 + 10
x = 146
So, the two angles are 146 degrees and 34 degrees.