00:01
So let's start off by knowing that angle bac is half of the measure of the arc b .c.
00:05
So we can connect those two into an equation to x is equal to one half the measure of 6y.
00:14
And if we multiply these two together, we get 2x is equal to 3y, divide by 2, divide by 2, x is equal to 3 over 2 y.
00:27
So now let's try to find the other measurements.
00:31
We know that all three arcs are labeled and all three arcs added together makes 360.
00:35
So let's make an equation connecting all three arcs together, 6y plus 6y plus 4x.
00:43
But i can substitute this value in for x, 3 over 2y.
00:48
And all that is going to equal 360.
00:51
6y and 6y is 12y, 4 times 3 over 2y becomes 3 .2y.
00:57
6y equals 360.
01:03
Add these together, we get 18y equals 360, divide by 18, divide by 18, and y is equal to 20.
01:18
We can take this y out, replace it with 20, 3 over 2 times 20, and x is equal to 30.
01:27
So those are our two values of x and y.
01:30
Now let's find each of our arc and angle measurements...