Question

find the value of each variable

x=38, y=76

x=52, y=76

x=38, y=104

x= 52, y= 104

Answer 1

x = 38, y = 104

opposite angles are always equal, so do 76/2, get 38. then do 76*2 to get 152. You take 152 from 360 (the total number of degrees in it) then divide that by 2 to get y, 104

Answer 2

Answer:  The correct option is

(C) x = 38  and  y = 104.

Step-by-step explanation:  We are given to find the values of the variables x and y from the figure.

We know that

if two angles make a linear pair, then the sum of their measures is 180°.

From the figure, we note that

the angles with measures y° and 76° makes a linear pair, so we have

$y^\circ+76^\circ=180^\circ\\\\\Rightarrow y+76=180\\\\\Rightarrow y=180-76\\\\\Rightarrow y=104.$

Also, the angles with measures 2x° and y° makes a linear pair, so we have

$2x^\circ+y^\circ=180^\circ\\\\\Rightarrow 2x+y=180\\\\\Rightarrow 2x=180-104\\\\\Rightarrow 2x=76\\\\\Rightarrow x=\dfrac{76}{2}\\\\\Rightarrow x=38.$

Thus, the required values the variables are x = 38 and y = 104.

Option (C) is CORRECT.