Question

in the given figure, AECD is a parallelogram and angle DAB + angle DCB = 180°. The measure of angle AEC is equal to​

Answer 1

Answer:

Given, ∠BAE=30o,∠BCE=10o

∠DAB+∠DCB=180o

And ∠DAB+∠DCB=180o

⇒(∠DAE+∠BAE)+(∠DCE−∠BCE)=180o

⇒∠DAE+30o+∠DCE−10o=180o

⇒∠DAE+∠DCE+20o=180o

⇒∠DAE+∠DCE=180o−20o

⇒∠DAE+∠DAE=160o[∵∠DAE=∠DCE,oppositeanglesoftheparallelogram]

⇒2∠DAE=160o⇒∠DAE=80o

For parallelogram AECD,

∠DAE+∠AEC+∠DCE+∠ADC=360o

⇒∠DAE+∠DCE+∠AEC+∠ADC=360o

⇒160o+∠AEC+∠AEC=360o[∵∠AEC=∠ADC,oppositeanglesoftheparallelogram]

⇒2∠AEC=360o−160o

⇒2∠AEC=200o

⇒∠AEC=100o

Hence,∠AEC=100o.

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Answer 2

||✪✪ QUESTION ✪✪||

in the given figure, AECD is a parallelogram and angle DAB + angle DCB = 180°. The measure of angle AEC is equal to

|| ✰✰ ANSWER ✰✰ ||

Refer To Image First..

Extra Knowledge :-

There are six important properties of parallelograms to know:

→ Opposite sides are congruent .

→ Opposite angels are congruent .

→ Consecutive angles are supplementary .

→ If one angle is right, then all angles are right.

→ The diagonals of a parallelogram bisect each other.