Question

please answer this question by process​

Answer 1

Step-by-step explanation:

Given :-

angle DCE = 80° , angle CEA = 30°

angle BAE = 130°, angle AEF = 50°

To find :-

Prove that AB || CD ?

Solution :-

Given that

angle DCE = 80° ,

angle CEA = 30° ,

angle BAE = 130°,

angle AEF = 50°

From the given figure ,

Angle BAE + angle AEF

=> 130°+50°

=> 180°

Angle BAE + angle AEF = 180°

angle BAE and angle AEF are the interior angles on the same side to the side AE on AB and EF

and they are Supplementary angles.

We know that

If the interior angles on the same side to the transversal are supplementary then the two lines are parallel lines.

Therefore, AB || EF ---------(1)

and AE is the transversal.

From the given figure,

80° = 30° + 50°

angle DCE = angle CEA + angle AEF

angle DCE = angle CEF

angle DCE and angle CEF are the interior angles either side of the side CE which are not adajacent angles

=> angle DCE and angle CEF are alternative interior angles

Where CE is the transversal.

We have Alternative interior angles are equal

Therefore, CD || EF ----------(2)

and CE is the transversal

We know that

If two lines Parallel to another line then the two lines are parallel lines.

We have , from (1) &(2)

AB || EF and CD || EF => AB || CD

Hence , Proved.

Answer :-

AB || CD

Used formulae:-

• If corresponding angles are equal then the two lines are parallel lines.
• If alternative interior angles are equal then two lines are parallel lines.

Points to know :-

• If a line Intersects two lines at two or more than two points is called a transversal.
• If two parallel lines Intersected by a transversal then
• Corresponding angles are equal.
• Alternative interior angles are equal.
• Interior angles on the same side to the transversal are supplementary.
• Exterior angles on the same side to the transversal are supplementary.

Answer 2

Step-by-step explanation:

Here, /_ IAE + /_BAE=180° ( linear pair)

/_ IAE =180°- /_ BAE

/_ IAE =180°-130°

/_ IAE =50°

So, AB ll EF and transversal AE as /_IAE=/_AEF which is alternate interior angles of line AB and EF.

Now, /_IEF= 30°+50°

/_IEF= 80°

And, /_CIB=/_IEF (Corresponding angles)

/_CIB=80°

So, here, /_DCI=/_CIB

Therefore,CD II AB as there alternate interior angles are equal.