Question

Please help me understand this
A, B, C & D form the vertices of a quadrilateral.
A, B & F lie on a straight line.
C, B & E lie on a straight line.
Find the value of the angle x

Answer 1

Answer:

Value of x=144°

Step-by-step explanation:

Consruction:

Consider point Z such that Z-B-A-F

Angle FBE=53°

Angle CBA=53°.........vertically opposite angles

Angle BCD=90...........given

Angle DAZ=107...........given

Angle DAB=180-angle DAZ....... Linear pair

Angle DAB=180-107

Angle DAB=73°

Angle DAB+angle ABC+angle BCD+angle CDA=360°.......sum of all angles of quadrilateral is 360°

73+53+90+x=360

216+x=360

x=360-216

x=144°

Value of x=144°

Answer 2

Answer:

x= 144°

Step-by-step explanation:

1) Apply Property of linear pair of angles on line A -B-F i.e. 180-107 = 73

2) similarly apply on line C-B-E i.e. 180- 53 = 127

3) angle CBF+ angle CBA = 180

127 +angle CBA =180

180-127= 53

4) 73 +53+90+x=360

216 + x = 360

x = 360 -216

x= 144