Angle C and Angle D are supplementary angles. If the measure of Angle D is nine less than twice the measure of Angle C, find the measure of Angle D.
PLEASE HELP!!! I have no idea where to even start!
D= 117
C= 63
Why did the angle refuse to tell the other angle its measurement?
Because it wanted to keep them in suspense!
But don't worry, I'm here to help. Let's solve this riddle of angles, shall we?
We know that supplementary angles add up to 180 degrees. So, we can set up an equation to represent the relationship between Angle C and Angle D.
Let's say x represents the measure of Angle C. According to the problem, Angle D is nine less than twice the measure of Angle C, which can be expressed as 2x - 9.
Since Angle C and Angle D are supplementary, we have the equation:
x + (2x - 9) = 180
Now, we can simplify and solve the equation:
3x - 9 = 180
3x = 189
x = 63
So, the measure of Angle C is 63 degrees.
To find the measure of Angle D, we substitute x back into the expression for Angle D:
2x - 9 = 2(63) - 9 = 117
Therefore, the measure of Angle D is 117 degrees. Voila!
To find the measure of Angle D, we need to set up an equation based on the given information.
Let's assume that the measure of Angle C is x.
According to the problem, Angle D is nine less than twice the measure of Angle C. Therefore, we can express the measure of Angle D as 2x - 9.
Since Angle C and Angle D are supplementary angles, their measures add up to 180 degrees.
So, we can set up the equation as follows:
Angle C + Angle D = 180
Substituting the expressions we found for Angle C and Angle D:
x + (2x - 9) = 180
Combining like terms:
3x - 9 = 180
Adding 9 to both sides of the equation:
3x = 189
Dividing both sides by 3:
x = 63
Now that we know the measure of Angle C is 63 degrees, we can find the measure of Angle D:
Angle D = 2x - 9
Angle D = 2(63) - 9
Angle D = 126 - 9
Angle D = 117
Therefore, the measure of Angle D is 117 degrees.
To find the measure of Angle D, we can start by setting up the problem using algebraic expressions and equations.
Let's denote the measure of Angle C as x.
According to the problem, Angle D is nine less than twice the measure of Angle C. This can be represented as:
D = 2C - 9
We also know that Angle C and Angle D are supplementary angles, which means that their measures add up to 180 degrees. So, we have the equation:
C + D = 180
Now, we can substitute the expression for D from the first equation into the second equation:
C + (2C - 9) = 180
Combine like terms:
3C - 9 = 180
Add 9 to both sides of the equation:
3C = 180 + 9
3C = 189
Finally, divide both sides of the equation by 3 to solve for C:
C = 189 / 3
C = 63
Therefore, the measure of Angle C is 63 degrees.
To find the measure of Angle D, substitute the value of C back into either equation:
D = 2C - 9
D = 2(63) - 9
D = 126 - 9
D = 117
So, the measure of Angle D is 117 degrees.
"Angle D is nine less than twice the measure of Angle C"
D = 2C - 9
and we know C+D = 180 , so .....