SOLUTION: Alright, well I'm not sure if this is a geometric formula, but I don't understand how to find the measures of two supplementary angles. Angle ABD=5x and angle BDE=(17x-18) How Am I

Click here to see ALL problems on Geometric formulas

Question 517445: Alright, well I'm not sure if this is a geometric formula, but I don't understand how to find the measures of two supplementary angles. Angle ABD=5x and angle BDE=(17x-18) How Am I supose to start this?
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
I don't understand how to find the measures of two supplementary angles.
Angle ABD=5x and angle BDE=(17x-18)

-----------------
Supplementary angles have a sum of 180 degrees.
-----
Equation:
5x + 17x-18 = 180
22x = 162
x = 7.3636
----
ABD = 5x = 36.82 degrees
---
BDE = 17x-18 = 107.18 degrees
===============================
Cheers,
Stan H.
==============

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You are told that the two angles are supplementary. That means that when you add the measures of these two angles, the resulting sum will be 180 degrees. (That's the definition of supplementary angles ... two angles that when added result in 180 degrees.)
.
One of the angles has a measure of 5x. The other has a measure of 17x - 18. Add them together as follows:
.
5x + 17x - 18
.
and set this sum equal to 180 degrees:
.
5x + 17x - 18 = 180
.
Add together the two terms that contain x:
.
22x - 18 = 180
.
Get rid of the -18 on the left side by adding 18 to both sides:
.
22x = 198
.
Solve for x by dividing both sides by 22:
.
x = 198/22 = 9
.
x = 9 degrees
.
So the angle that has a measure of 5x equals 5 times 9 degrees or 45 degrees. Since its supplement is the angle that when added to the 45 degrees gives a total of 180 degrees. We can find the second angle by subtracting 45 from 180 and get the answer of 135 degrees. The two angles are ABD = 45 and BDE = 135 degrees.
.
We can also check the value of angle BDE by calculating 17x - 18. We now know that this answer should be 135 degrees, but let's work it out anyhow:
.
17x - 18 = ?
.
Substitute 9 for x:
.
17*9 - 18 = ?
.
Multiply out the first term:
.
153 - 18 = ?
.
Do the subtraction to get the answer of 135. Yup. It checks out with the answer that we got by subtracting the first angle (45 degrees) from 180 degrees.
.
Hope this helps you to see your way through this problem. An added note ... check the labeling of the second angle. I would have thought that it was DBE so that B was the common vertex of the two angles. That way line ABE would have been a straight line (indicated by the 180 degrees). This does not affect the answer that is calculated above.
.