I have a pair of supplementary angles, the measure of one angle is 8 times the measure of the other. What is the measure of the larger angle?

What is the measure of the smaller angle?

Let x = the smaller angle

x + 8x = 180
9x = 180
x = 20

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Well, isn't that a great pair of angles! Let's call the smaller angle x. Since the larger angle is 8 times the measure of the smaller angle, we can say the larger angle is 8x.

Now, we know that supplementary angles add up to 180 degrees. So we can write an equation:

x + 8x = 180

Simplifying it,
9x = 180

Dividing both sides by 9, we find that x is 20.

So the smaller angle is 20 degrees, and the larger angle is 8 times that, which is 160 degrees.

They make quite the dynamic duo, don't they?

To find the measure of the larger angle, let's first assume that the smaller angle measures x degrees. Since the two angles are supplementary, we know that the sum of their measures is 180 degrees.

So, if the smaller angle measures x degrees, the larger angle must measure 8x degrees.

To find the value of x, we can set up the equation:

x + 8x = 180

Combining like terms, we have:

9x = 180

Now, we can solve for x by dividing both sides of the equation by 9:

x = 20

Therefore, the measure of the smaller angle is 20 degrees.

To find the measure of the larger angle, we can substitute the value of x into the equation we set up earlier:

8x = 8 * 20 = 160

So, the measure of the larger angle is 160 degrees.