Answer:
angle X = angle Y = 66 degree
x = y = 11
Step-by-step explanation:
[tex]In\:\triangle WXY:\\
WX = WY ...(given)\\
\therefore m\angle X = m\angle Y....(1)\\
\therefore (6y-2)\degree= (4x+20)\degree....(2)\\[/tex]
By interior angle sum postulate of a triangle:
[tex]m\angle X +m\angle Y+m\angle W = 180\degree\\
\therefore (6y -2)\degree+ (4x+20)\degree+52\degree= 180\degree\\
\therefore (6y -2)\degree+ (4x+20)\degree= 180\degree-52\degree\\
\therefore (6y -2)\degree+ (4x+20)\degree= 128\degree.....(3)\\
From\: equations\: (2)\: and \: (3)\\
(4x+20)\degree+ (4x+20)\degree= 128\degree\\
\therefore (8x+40)\degree= 128\degree\\
\therefore 8x+40= 128\\
\therefore 8x= 128-40\\
\therefore 8x= 8\\
\therefore x= \frac{88}{8} \\
\huge\red{\boxed{\therefore x= 11}}\\\\
\because (6y-2)\degree = (4x+20)\degree\\
\therefore 6y - 2 = 4\times 11+20\\
\therefore 6y = 44 + 20 + 2\\
\therefore 6y = 66\\
\therefore y = \frac{66}{6}\\
\huge \purple{\boxed{\therefore y = 11}}\\
m\angle X = m\angle Y = (4x+20)\degree...(from \: 1)\\
\therefore m\angle X = m\angle Y = (4\times 11+20)\degree\\
\therefore m\angle X = m\angle Y = (44+20)\degree\\
\huge\orange{\boxed{\therefore m\angle X = m\angle Y = 64\degree}}\\[/tex]
