Question

Find the missing values of the variables. The diagram is not to scale.

A.
x = 75, y = 101

B.
x = 91, y = 75

C.
x = 101, y = 125

D.
x = 75, y = 91

Answer 1

The answer is B.

To find y, it is 105 +y = 180 (striaght line)

y = 75. In the options above only 'b' has y = 75.

Answer 2

The answer is the option B

`x=91\°,y=75\°`

Explanation:

we know that

The sum of the internal angles of the polygon is equal to

`S=(n-2)*180\°`

where n is the number of sides

In this problem

`n=2`

so

substitute

`S=(4-2)*180\°=360\°`

Step 1

Find the value of y

`105\°+y\°=180\°` -------> by supplementary angles

Solve for y

`y=180\°-105\°=75\°`

Step 2

Find the value of x

The sum of the internal angles of the polygon is equal to
`360\°`

so

`125\°+69\°+75\°+x=360\°`

Solve for x

`269\°+x=360\°`

`x=360\°-269\°=91\°`