The directions that came with the kite pattern that Andre ordered on the internet said to cut out 2 supplementary angles so that the measure of one is twice the measure of the other. How many degrees are in each angle? Justify your answer.

a + 2a = 180

3a = 180
a = 60

The smaller angle has 60 degrees.

But how do you get 60?

180 divided by 3 = 60

But aren't there only 2 angles? I'm confused.

Yes there are two angles. One is 60 degrees. Your problem states that the other one is twice the measure of the first.

2 times 60 = 120

1 angle measures 60 degrees.
The other angle measures 120 degrees.

To solve this problem, we need to understand what it means for angles to be supplementary and how their measures relate.

First, let's define what supplementary angles are. Supplementary angles are two angles that add up to 180 degrees. In other words, if we have angle A and angle B, and A + B = 180 degrees, then A and B are supplementary angles.

Now, according to the kite pattern's instructions, we need to cut out two supplementary angles such that one angle's measure is twice the measure of the other.

Let's name the smaller angle as "x" degrees. Since the larger angle is twice the measure of the smaller angle, we can write it as "2x" degrees.

Since the angles are supplementary, the sum of their measures is 180 degrees. So we can write the equation: x + 2x = 180.

To solve this equation, we combine like terms: 3x = 180.

Dividing both sides of the equation by 3, we find that x = 60.

Therefore, the smaller angle measures 60 degrees, and the larger angle measures 2 times that, or 120 degrees.

To summarize, in the kite pattern, the measure of the smaller angle is 60 degrees, and the measure of the larger angle is 120 degrees.