Question

Please answer question C.

Answer 1

`<x = 40`

Explanation:

The degree measure of a line is (180) degrees. Therefore the sum of (<x), (<y), and (<z) is (180) degrees. As per the given information (<y = 80). Moreover, it is given that the angles (x) and (z) are in the following ratio: ( (<x) : (<z) = (2) : (3) ). Call (n) the factor by which the ratio was simplified. Using this though process, one can state the following: ( (<x) = 2n) and ( (<z) = 3n). Using all of this information, form an equation, solve for (n), finally substitute and solve for (<x).

`(<x)+(<y)+(<z)=180`

Substitute,

`2n+3n+80=180`

Simplify,

`5n+80=180`

Inverse operations,

`5n+80=180`

`5n=100`

`n=20`

Substitute to back solve for (<x),

`<x = 2n\\n = 20\\\\<x = 2(20)\\<x = 40`

Answer 2

First you can subtract y from 180 (number of degrees in a straight line) to find the value of x and z combined; 180-80=100. This means x+z=100.

Since you know that x:z is 2:3, and they add up to 100, you can find x and z. Add 2+3 (the ratios) to get 5. There are 5 parts in 100. The value of each part is 20 (divide 100/5). The value of x is 2 parts, and the value of z is 3 parts. 2 parts of 20 is 40 (multiply 2*20). 3 parts of 30 is 60 (multiply 3*20).

Now you know that x is 40 and y is 60.

You can also check your answer.

40+80+60 equals 180.