By Team Aakash Byju's | 31st December 2022
The value of x in the given image is 50°.
x
50°
Given that the image ABCD represents a rectangle. It is known that the diagonals of a rectangle are congruent and bisect each other.
AC = BD
=>AP = PC = DP = PB
We know that the sum of all interior angles of a triangle is 180°. Also in ΔAPB, AP = PB and the opposite angles of these sides are equal we can write ∠ABP = ∠PAB
Also, ∠APB = 100° and ∠APB + ∠ABP + ∠PAB = 180°
=> 100 + ∠ABP + ∠PAB = 180° => ∠ABP + ∠ABP = 80° (∵ ∠ABP = ∠PAB)
=> 2∠ABP = 80° => ∠ABP = ∠PAB = 40°
Since AC is a straight line. ∠APC = 180°
Further, ∠APB = 100° => ∠APB + ∠BPC = 180°
=> 100° + ∠BPC = 180° => ∠BPC = 80°
Since it is noted that PC = BP, the opposite angles ∠PBC = ∠BCP.
Also, ∠BPC + ∠PBC = ∠BCP = 180°
=> 80° + ∠PBC + ∠PBC = 180° (∵ ∠PBC = ∠BCP)
=> 2∠PBC = 100° => ∠PBC = ∠BCP = 50° => x = ∠BCP = 50°