The difference between two supplementary angles is 10º. Find the acute angle.

Answer 1

The definition of supplementary angles is that the two angles add up to 180. Let's call the angles angle x and angle y, so that x + y = 180 degrees.

We also know that the difference between these two angles is 10 degrees. Therefore we can say that x - y = 10. Now we have a system of equations.

To solve the system of equations, let's first solve for x in the second equation (you can solve for y as well, whichever makes it easier for you). This gives us the equation: x = 10 + y.

Now that we have that, we can plug in "10+y" for the x in the first equation to get:

(10+y) + y = 180.

Now we just have to solve for y:

(10+y) + y = 180 --> 10 + 2y = 180 --> 2y = 180-10 --> 2y = 170 --> y = 170/2 --> y = 85

Now that we have solved for y, we can plug in the value of 85 for y into the second equation (x-y = 10) to get (x-85 = 10) We can then solve for x to get x = 95.

Now that we have solved for the two angles:

x = 95 and y = 85, we can tell that 85 is the acute angle because it is the angle that is less than 90 degrees.

Answer 2

Supplementary angles add up to 180 degrees

Acute angles are less than 90 degrees

So,

Acute angle can be x-10 and the other angle can be x

We can use the equation

x-10 +x = 180

2x - 10 + 180

2x = 190

x= 95

Plug into the acute angle formula x-10= 95 -10

The acute angle is 85 degrees