Question

D 45° y-- 35° 25° E F G 2x - 10° H

Answer 1

Given:

1) the angle FGD and angle DGE are supplementary angles.

`\begin{gathered} \angle FGD+\angle DGE=180^(\circ) \\ y-35^(\circ)+25^(\circ)=180^(\circ) \\ y-10^(\circ)=180^(\circ) \\ y=190^(\circ) \end{gathered}`

Also the line DE is parallel to GH and angle EDG and DGH formed supplementary angles.

`\begin{gathered} \angle EDG+\angle DGE+\angle EGH=180^(\circ) \\ 45^(\circ)+25^(\circ)+2x-10^(\circ)=180^(\circ) \\ 60^(\circ)+2x=180^(\circ) \\ 2x=120^(\circ) \\ x=60^(\circ) \end{gathered}`

Answer: x = 60 degree, y = 190 degree

2) the pair of angles of interior angles on the same sideof the transversal area supplementary.

`\begin{gathered} 3x+x=180^(\circ) \\ 4x=180^(\circ) \\ x=45^(\circ) \end{gathered}`

Answer: x = 45 degree.

3) The angle BEC and CEA are supplimetary angles.

`\begin{gathered} \angle BEC+\angle DEC+\angle DEA=180^(\circ) \\ 90^(\circ)+\angle DEC+x=180^(\circ) \\ \angle DEC=90^(\circ)-x \end{gathered}`

4) Angle GLK and angle EKL are supplementary,

`\begin{gathered} \angle GLK+\angle EKL=180^(\circ) \\ \angle GLK+x=180^(\circ) \\ \angle GLK=180^(\circ)-x^{} \end{gathered}`

5) B is parallel to D . and angle formed GFE and angle FED are supplementary,

`\begin{gathered} \angle GFE+\angle FED=180^(\circ) \\ 40^(\circ)+5x+65^(\circ)=180^(\circ) \\ 5x=75^(\circ) \\ x=15^(\circ) \end{gathered}`

Answer: x = 15 degree.

6) angle ABC and angle BCD are alternate angles and so they are equal.

`\begin{gathered} \angle ABC=\angle BCD \\ x+15^(\circ)=45^(\circ) \\ x=45^(\circ)-15^(\circ) \\ x=30^(\circ) \end{gathered}`

Answer: x = 30 degree.