Algebra 2, If the measure of one angle is five less than two-thirds of the measure of its supplementary angle?

Question

If the measure of one angle is five less than two-thirds of the measure of its supplementary angle . Find the measure of the angles?

Answer 1

x+y=180
x=2y/3 - 5

try to find the value of x and y

Answer 2

Let x = measure of one angle, then
180 - x = other angle (by definition of supplementary)
x = (2/3)(180-x) - 5
Multiply everything by 3
3x = 2(180-x) - 15
3x = 360 - 2x - 15
3x = 345 - 2x
5x = 345
x = 345/5
x = 69
180 - x = 180 - 69 = 111
Answer: The angles are 69 and 111

Let's check the answer just to be sure.
two-thirds of 111 is (2/3)(11) = 74
74 - 5 = 69
and 69+111 = 180

Answer 3

Let one angle be x. Then the other is 2x/3 - 5. Thease two are supplementary. That means,

x + (2x/3 -5) = 180
x+2x/3 = 185
5x/3 = 185
x = 111, and the other angle i.e. 2x/3 - 5 = 69
The angles are 111 and 69. Cross-check .... 111+69=180

Answer 4

Let measure of angle be x.
The angle plus its supplementary adds up to 180, so the supplementary angle is 180 - x.

Translating the problem statements into formulaic terms:

measure of one angle is:
x =

5 less than 2/3 measure of its supplementary angle:
(2/3)(180 - x) - 5

So x = (2/3)(180 - x) - 5

From there it is simple algebra problem.

Answer 5

2/3x+x=180 1 2/3x = 180 x=108 One angle=108, the other=72

Answer 6

let an angle be x
then the other angle could be represented as y,
where y= 2/3x-5
Definition of sup angles is they add up to 180 degrees, so
x+y=180,
substitute in for y the equation above.
x+2/3x-5=180
5/3x-5=180, add 5 to each side
5/3x=185, multiple both sides by 3
5x=555, divide both sides by 5
x=111.
plug this back into the equation above
y=2/3x-5
y=(2/3)(111)-5
y=74-5,
y=69.
So angle x is 111 degrees, angle y is 69 degrees.
Check: they both add up to 180 degrees.

Answer 7

x=2/3(180-x)-5
x+5=120-2/3x
5/3x=115
x=115(3/5)
=69*