Question

In this figure AB||CD, angle ABM= 40° angleCDM=35° find x....... with full explanation​

Answer 1

Given:

$AB||CD\\ \angle ABM= 40^\circ\\\angle CDM=35^\circ$

To find:

$x = ?$

OR

Major $M \angle M= ?$

Solution:

First of all, let us make a construction:

Draw another line parallel to AB and CD from point M to point N as shown in the attached figure.

Now, as per attached figure:

• CD || MN.

• Line MD cuts both the lines.

$\therefore \angle CDM = \angle DMN$ ($\because$ they are the alternate angles)

$\therefore \angle CDM = \angle DMN = 35^\circ$

Similarly,

• AB || MN.

• Line BM cuts both the lines.

$\therefore \angle ABM = \angle NMB$ ($\because$ they are the alternate angles)

$\therefore \angle ABM = \angle NMB= 40^\circ$

Now, we can see that point M is made of two angle $minor \angle M$and $major \angle M$.

$Minor \angle M = \angle DMN + \angle NMB = 35^\circ + 40^\circ = 75^\circ$

$minor \angle M + major \angle M = 360^\circ\\\Rightarrow 75^\circ+ major \angle M = 360^\circ\\\Rightarrow 75^\circ+ x = 360^\circ\\\Rightarrow x = 360^\circ - 75^\circ\\\Rightarrow x = 285^\circ$

So, the answer is:

$x=285^\circ$