Question

In a parallelogram ABCD, side DC is produced to E and angle BCE=105 degrees. Find angles A, B, C and D.

Answer 1

Answer:

Parallelogram:

L BCE=105 degree

LA=105 degree

LB = 180-105=75 degree

LD=75 degree

Answer 2

Angle A=Angle C=75 degrees, Angle B=Angle D=105 degrees

Step-by-step explanation:

In parallelogram ABCD

Angle BCE=105 degrees

By property of parallelogram

Angle A=Angle C, Angle B=Angle D

By attached figure

Angle BCE+angle C=180 degrees

Reason: Linear pair

Substitute the values

$105+\angle C=180$

$\angle C=180-105=75^{\circ}$

Angle C+angle B=180 degrees

Reason: Sum of interior angles on the same side is equal to 180 degrees

$75+\angle B=180$

$\angle B=180-75=105 degrees$

Angle A=Angle C=75 degrees, Angle B=Angle D=105 degrees

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