Question

An angle at one corner of an envelope is given below.
If the envelope is in the shape of a parallelogram, find the value of ∠ADC.

• A. ${75}^o$
• B. ${95}^o$
• C. ${65}^o$
• D. ${85}^o$

Answer 1

The correct option is C ${65}^o$

Properties of a parallelogram:
(1) Opposite sides are equal.
(2) Opposite sides are parallel to each other.
(3) Opposite angles are equal.
(4) Sum of adjacent angles is 180°.

In the parallelogram ABCD:
∠DAB and ∠ADC are adjacent angles.
So, they act as co-interior angles.

∴ ∠DAB + ∠ADC = 180°
⇒ 115° + ∠ADC = 180°
⇒ ∠ADC = 180° – 115° = 65°

So, ∠ADC = 65°