angles ABC and XYZ are complementary angles. if m < ABC is 18 more than three times m < XYZ, find < XYZ
i have no idea how to do this i know that something has to equal 18+ 3m but i don't understand the (<) sings
Oh, don't worry, < is just the symbol for an angle. So, let's break it down. We know that angles ABC and XYZ are complementary angles, which means that when you add them together, they equal 90 degrees.
Let's represent the measure of angle XYZ as x. According to the problem, the measure of angle ABC is 18 more than three times the measure of angle XYZ. So, we can write it as:
m < ABC = 18 + 3m < XYZ
To solve for x, we can set up an equation.
m < ABC + m < XYZ = 90
18 + 3x + x = 90
4x = 72
x = 18
So, the measure of angle XYZ is 18 degrees.
To solve this problem, we need to use the fact that complementary angles add up to 90°.
Let's assign variables to the angles:
Let <ABC = x
Let <XYZ = y
According to the problem, we know that the angles are complementary, so we can write the equation:
x + y = 90°
It is also given that the measure of <ABC is 18 more than three times the measure of <XYZ, which can be written as:
x = 3y + 18
Now we can solve this system of equations to find the value of <XYZ (y).
1. Substitute the value of x from the second equation into the first equation:
(3y + 18) + y = 90
2. Combine like terms:
4y + 18 = 90
3. Subtract 18 from both sides of the equation:
4y = 90 - 18
4y = 72
4. Divide both sides of the equation by 4:
y = 72 / 4
y = 18
So, the measure of angle XYZ (<XYZ) is 18 degrees.
To solve this problem, we need to understand what it means for angles to be complementary. Complementary angles are two angles that add up to 90 degrees.
Let's assign variables to the angles:
ABC = angle ABC
XYZ = angle XYZ
We are given that ABC and XYZ are complementary, which means:
ABC + XYZ = 90 degrees
We are also given that the measure of angle ABC (m < ABC) is 18 more than three times the measure of angle XYZ (3m < XYZ).
In mathematical terms, this can be written as:
m < ABC = 3m < XYZ + 18
Now we can set up an equation using the information we have:
ABC + XYZ = 90
Substitute ABC with 3m < XYZ + 18:
(3m < XYZ + 18) + XYZ = 90
Simplify by combining like terms:
3m < XYZ + XYZ + 18 = 90
Combine the terms on the left side of the equation:
4m < XYZ + 18 = 90
Subtract 18 from both sides to isolate the term with m:
4m < XYZ = 90 - 18
4m < XYZ = 72
Now, divide both sides of the equation by 4 to solve for m < XYZ:
m < XYZ = 72 / 4
m < XYZ = 18
Therefore, the measure of angle XYZ is 18 degrees.
"<" indicates that the previous value is LESS than the following value.
">" indicates that the previous value is MORE than the following value.