If two supplementary angles are in the ratio 2:7, then angles are

Answer 1

Hello, let's review the meaning of supplementary angles. They are angles that add up to a total of 180 degrees. We know that the two angles must equal 180 degrees, and must also have a ratio of 2:7. Let's think about this using some basic algebra.

The ratio 2:7 can be applied extended to represent 2x:7x for any number x. See below:

x = 2; 4:14

x=5; 10:35

These examples follow the 2:7 ratio. We want to find the ratio 2x : 7x that allows us to add the two numbers and get 180. We can set up an algebraic equation to do this:

2x + 7x = 180 <-- solve for x. Start by combining like terms.

9x = 180 <-- divide both sides by 9

x = 20.

What are our two angles when x = 20?

2 (20) = 40

7 (20) = 140

CHECK:

40+140 = 180 correct

Do 40 and 140 follow the given ratio? Yes!