Question

if ABIIDE, angle ABC=115º and angle BCD=55°, then find the value of x​

Answer 1

BCD = 35°

Step-by-step explanation:

Given information:

ABC = 55°

CDE = 160°

AB is parallel to DE.

We can extend the line DE towards the line BC as shown in the image attached below.

Let the point that DE meets BC be F.

From the figure,

ABE = BED (Alternate angles)

Therefore, BED = 55°

BED + CED = 180° (Since, BC is a straight line)

=> 55° + CED = 180°

=> CED = 180 - 55 = 125°

Also,

FDC + CDE = 180° (Since, FE is a straight line)

=> FDC + 160° = 180°

=> FDC = 180° - 160° = 20°

Now,

CED + FDC + BCD = 180° (Sum of the angles of a triangle = 180°)

125° + 20° + BCD = 180°

=> BCD = 180° - (125° + 20°)

=> BCD = 180° - 145°

=> BCD = 35°

Answer 2

Answer:

120°

Step-by-step explanation:

Solving Method -

∠BCD = ∠ABC - (180 -∠CDE)

55 = 115 - (180 - x)

55 = 115 - 180 + x

55 = - 65 + x

55 + 65 = x

120 = x

x = ∠CDE = 120°

Chking Method -

∠BCD = ∠ABC - (180 - ∠CDE)

∠BCD = 115 - (180 - 120)

∠BCD = 115 - 60

∠BCD = 55

55 = 55

LHS = RHS

Hope it helps you mate..

:)