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.