2 angles are supplementary. The larger angle measures 15 degrees less than twice the smaller. Whats the degree measure of each angle?
step by step explaination please!!
2007-03-29 07:19:33 · 12 answers · asked by aviator 5 in Science & Mathematics ➔ Mathematics
Suplementary angles are angles in which their sums add up to 180 degrees so:
x + (2x -15) = 180
3x - 15 = 180
3x = 195
x = 65 (The smaller angle)
The larger angle is 180 - 65 = 115.
2007-03-29 07:26:47 · answer #1 · answered by Justin M 4 · 1⤊ 0⤋
Hi,
Supplementary angles are 2 angles that add to 180 degrees. If the smaller angle is x degrees, and the larger is 15 degrees less than twice the smaller, then it is represented by 2x - 15.
Adding those 2 angles together, you get
x+(2x-15)=180
Simplifying this:
3x - 15 = 180
3x = 195
x = 65 for the smaller angle
2x-15 = 2(65)-15=130-15=115 for the larger angle
You can see that these add to a80 and 115 is 15 less than twice 65.
I hope that helps!
2007-03-29 07:28:28 · answer #2 · answered by Pi R Squared 7 · 0⤊ 0⤋
Step 1: x+y=180 (supplementary angles=180)
Step 2: x=2y-15 (the larger of the angles)
Step 3: y=smaller angle
(2y-15) + y = 180
3y = 180 + 15
3y= 195
y = 65
x= 2(65)-15
x=130-15
x=115
Proof: x+y=180
115+65=180
2007-03-29 07:43:11 · answer #3 · answered by MMS47 1 · 0⤊ 0⤋
call x : smaller angle thus the larger angle is (180 - x), they are supplementary.
According to problem: the different between twice of smaller and larger is 15
2x - (180 - x) = 15
x= 65 ----> smaller
larger is 180 -65 = 115
2007-03-29 07:53:49 · answer #4 · answered by tuoidabuon 2 · 0⤊ 0⤋
If two angles are supplementary, the sum of the two is 180. The two angles are now x and (2x-15) The new equation becomes: x + (2x-15) = 180
Then (removing parentheses) x+2x-15=180
3x-15 = 180
3x=195
x = 65
The two angles are 65 and (2x65)-15 or 130-15=115
ANSWER: 65 degrees and 115 deggrees
2007-03-29 07:30:53 · answer #5 · answered by Rick T 1 · 0⤊ 0⤋
The angles are supplementary so if one of them can be x, then we can call the other one 180-x
larger angle is 15 deg less than twice the smaller
hence 180-x + 15 = 2x
195 = 3x
x = 195/3
The two angles are ...
x = 65
180-x = 115
2007-03-29 07:28:31 · answer #6 · answered by Orinoco 7 · 0⤊ 0⤋
Let the larger angle be "A" and the smaller angle be "B".
We know that:
A + B = 180
and we know that:
A - 15 = 2B --> A = 2B + 15
Then we stick this in the first equation and solve for B:
2B + 15 + B = 180
3B = 165
B = 55
Therefore, A = 180 - B = 180 - 55 = 125
Your angles are 125 degrees and 55 degrees.
Hope this helps!
2007-03-29 07:28:27 · answer #7 · answered by Josh 2 · 0⤊ 0⤋
x + 2x - 15 = 180
3x - 15 = 180
3x - 15 + 15 = 180 + 15
3x = 195
3x / 3 = 195 / 3
x = 195 / 3
x = 65°
The smaller angle is 65
180 - 65 = 115
The larger angle is 115 °
- - - - - - - -s-
2007-03-29 08:01:33 · answer #8 · answered by SAMUEL D 7 · 0⤊ 0⤋
assuming first angle is A and second is B
A + B = 180
now , assuming A is larger ,
A = 2B - 15
now substitute this equation into the 1st one
2B - 15 + B = 180
3B = 180 + 15 = 195
B = 65
again substitute
A = 2(65) - 15
A = 130 - 15
A = 115
A = 115 B = 65
2007-03-29 07:32:33 · answer #9 · answered by Anonymous · 0⤊ 0⤋
180 = x + y
x + 15 = 2y
.....
180 - x = y
x + 15 = 2y
.......
180 - x = y
x + 15 = 2(180 - x)
........
180 - x = y
x + 15 = 360 - 2x
.......
180 - x = y
x + 2x = 360 - 15
.........
180 - x = y
3x = 345
........
180 - x = y
345 / 3 = x
.........
180 - x = y
x = 115
.........
180 - 115 = y
x = 115
........
65 = y
x= 115
Answer: The larger angle measures 115 degrees and the other one measures 65 degrees.
I guess it is like that. Hope that helped. :-)
2007-03-29 07:36:56 · answer #10 · answered by Anonymous · 0⤊ 0⤋