Question

in the following figure, if ab//de, ‹abc= 115°and ‹bcd =55°,then find the measure of ‹cde​

Answer 1

Answer:

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°