Question

Find the measure of angles X and Y, as well as the values of x and y:

W
52 x
Х
(6y - 2)
(4x + 20)
Y

Answer 1

angle X = angle Y = 66 degree

x = y = 11

Explanation:

`In\:\triangle WXY:\\</p><p>WX = WY ...(given)\\</p><p>\therefore m\angle X = m\angle Y....(1)\\</p><p>\therefore (6y-2)\degree= (4x+20)\degree....(2)\\`

By interior angle sum postulate of a triangle:

`m\angle X +m\angle Y+m\angle W = 180\degree\\</p><p>\therefore (6y -2)\degree+ (4x+20)\degree+52\degree= 180\degree\\</p><p>\therefore (6y -2)\degree+ (4x+20)\degree= 180\degree-52\degree\\</p><p>\therefore (6y -2)\degree+ (4x+20)\degree= 128\degree.....(3)\\</p><p>From\: equations\: (2)\: and \: (3)\\</p><p> (4x+20)\degree+ (4x+20)\degree= 128\degree\\</p><p>\therefore (8x+40)\degree= 128\degree\\</p><p>\therefore 8x+40= 128\\</p><p>\therefore 8x= 128-40\\</p><p>\therefore 8x= 8\\</p><p>\therefore x= (88)/(8) \\</p><p>\huge\red{\boxed{\therefore x= 11}}\\\\</p><p>\because (6y-2)\degree = (4x+20)\degree\\</p><p>\therefore 6y - 2 = 4* 11+20\\</p><p>\therefore 6y = 44 + 20 + 2\\</p><p>\therefore 6y = 66\\</p><p>\therefore y = (66)/(6)\\</p><p>\huge \purple{\boxed{\therefore y = 11}}\\</p><p>m\angle X = m\angle Y = (4x+20)\degree...(from \: 1)\\</p><p>\therefore m\angle X = m\angle Y = (4* 11+20)\degree\\</p><p>\therefore m\angle X = m\angle Y = (44+20)\degree\\</p><p>\huge\orange{\boxed{\therefore m\angle X = m\angle Y = 64\degree}}\\`