Question

From the information given in the figure,find the value of x and y.

Answer 1

Explanation:

In
`\triangle ABC, \: AB \cong AC\\</p><p>\therefore m\angle ACB = m\angle ABC= 65\degree\\(\angle s\:opposite \:to\:equal\: sides) \\\\</p><p>AB \parallel DC.. (given) \\\</p><p>\therefore m\angle ABC= m\angle DCE= 65\degree\\(corresponding \:\angle s) \\\\</p><p>\therefore m\angle ACB+x+m\angle DCE = 180\degree \\\\</p><p>\therefore 65\degree+x+65\degree = 180\degree \\\\</p><p>\therefore x+130\degree = 180\degree \\\\</p><p>\therefore x= 180\degree -130\degree \\\\</p><p>\huge \red {\boxed {\therefore x= 50\degree}} \\\\`

Answer 2

65°*2 = 130° - since it's an isosceles triangle.

180- 130 = 50° (∠A, usually in the middle of 2 other letters ∠BAC) ( total angles in a triangle = 180° )

∠X = ∠BAC = 50° - since they are alternate angles

This is because of the parallel lines.

In this case we got a Z shape, so ∠x would be = ∠BAC