Question

15. In the figure, MN || AC. MO is the angle
bisector of angle AMN. What is the value of
x?
B
М.
N
500
X
A
0
C​

Answer 1

Solution -

Here, we have the information given that MN // AC and AB is the transversal .

So , we can state that -

Angle BMN = Angle BAC

So , angle BMN = 50°

Angle BMN and angle ANM form a linear pair .

So , angle AMN = 180° - 30°

=> Angle AMN = 150°

Angle AMO = ( Angle AMN ) / 2

=> Angle AMO = 75°

Now , we know that sum if all angles of a ∆ is 180°

So ,

x + 50 + 75 = 180°

=> x = 180° - 125 °

=> x = 55°

This is the required answer .

____________________

Answer 2

Answer:

AS MN is parallel to  AC

angle BMN=50*

Angle BMN and AMN from straight line(linear form)

let angle AMO is y

angle OMN is y   #angle bisector

2y+50=180

y=65  ------------  1

triangle AMO sum of interior angles is 180*

50+y+x=180

from 1

50+65+x=180

x=180- 115

x=65