Question

in the given figure prove that m || n​

Answer 1

Step-by-step explanation:

To prove;m||n

Hint:Angle FOA must equal Angle EAC ,for lines m and n to be parallel.

Solution:

Take ∆ ABC

We know that,according to angle sum property of triangle

Sum of internal angles of triangle is 180°.

$\angle \: ABC + \angle \: BCA + \angle \: CAB = 180° \\ \\ 45° + 40° + \angle \: CAB = 180° \\ \\ 85° + \angle \: CAB = 180° \\ \\ \angle \: CAB = 180° - 85° \\ \\ \bold{\angle \: CAB = 95°}$

Since BE is a straight line,so at point A ,linear pair is formed.

$\angle \: CAE + \angle \: CAB = 180° \\ \\ \angle \: CAE + 85° = 180° \\ \\\angle \: CAE = 180° - 95° \\ \\ \bold{\angle \: CAE = 85°}$

Thus,

Angle FOA = 85° [given]

Angle EAC=85° [Proved above]

Thus,both the angles are on straight line.

and

Angle FOA =Angle EAC=85°

Thus,

It is proved that m||n.

Hope it helps you.

To learn more on brainly:

1)2 lines M and n are parallel . find x and y in the diagram

https://brainly.in/question/14781719

Answer 2

Answer:

LA || MD

Step-by-step explanation:

angle LAD = angel MDB = 63