Question

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

Answer 1

Answer:

angle X = angle Y = 66 degree

x = y = 11

Step-by-step explanation:

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

By interior angle sum postulate of a triangle:

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