two angles are complementary one angle is 18 more than three times the other find the measure of the larger angle

x=24

x = 90 - y

x = 3 y + 18
---------------- subtract
0 = 72 - 4 y
y = 72/4 = 14
x = 90-14 = 76

Let's assume that one angle is represented by x degrees, and the other angle is represented by y degrees.

Given that the two angles are complementary, we know that the sum of the two angles is 90 degrees.

So, we can write the equation:
x + y = 90

We are also given that one angle is 18 more than three times the other angle. This can be written as:
x = 3y + 18

Now we can solve these two equations simultaneously to find the values of x and y.

Substitute the value of x from the second equation into the first equation:
(3y + 18) + y = 90
4y + 18 = 90
4y = 90 - 18
4y = 72
y = 72/4
y = 18

Substitute the value of y back into the second equation to find x:
x = 3(18) + 18
x = 54 + 18
x = 72

Therefore, the larger angle is 72 degrees.

To find the measure of the larger angle, we first need to set up an equation based on the given information.

Let's assume that one angle is represented by "x" and the other angle is represented by "y".

From the given information, we know that the angles are complementary, meaning they add up to 90 degrees. Therefore, we can write the equation:

x + y = 90.

We are also given that one angle is 18 more than three times the other. Mathematically, this can be written as:

x = 3y + 18.

Now we have a system of two equations:

x + y = 90, and
x = 3y + 18.

We can solve this system of equations using substitution or elimination. Let's use the substitution method.

Substitute the value of x from the second equation into the first equation:

(3y + 18) + y = 90.
4y + 18 = 90.
4y = 90 - 18.
4y = 72.
y = 72/4.
y = 18.

Now that we know the value of y, we can substitute it back into either of the original equations to find x:

x = 3(18) + 18.
x = 54 + 18.
x = 72.

Therefore, the larger angle measures 72 degrees.