heshott91
contestada

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

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 class=

Respuesta :

msyatham
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.
calculista

Answer:

The answer is the option B

[tex]x=91\°,y=75\°[/tex]

Step-by-step explanation:

we know that

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

[tex]S=(n-2)*180\°[/tex]

where n is the number of sides

In this problem

[tex]n=2[/tex]

so

substitute

[tex]S=(4-2)*180\°=360\°[/tex]

Step 1

Find the value of y

[tex]105\°+y\°=180\°[/tex] -------> by supplementary angles

Solve for y

[tex]y=180\°-105\°=75\°[/tex]

Step 2

Find the value of x

The sum of the internal angles of the polygon is equal to [tex]360\°[/tex]

so

[tex]125\°+69\°+75\°+x=360\°[/tex]

Solve for x

[tex]269\°+x=360\°[/tex]

[tex]x=360\°-269\°=91\°[/tex]