Question

an exterior angle of a parallelogram is 110°. Find the angles of the parallelogram​

Answer 1

Answer:

All the angles of the parallelogram are

<A = 110°

<B= 70°

<C= 110°

and<D=70°

Answer 2

Exterior angles of parallelogram = 110° (given)

D+C=180

C=180−110

=70

D=A (Opposite anɡels of ∣∣ɡm)

A=110

C=B (Opposite anɡelsbof ∣∣ɡm)

70°+70°

B=70°

∴ A=110°

B=70°

C=70°

D=110°

OR

SOLUTION :

ABCD is a parallelogram.

\angle{CBX}∠CBX is exterior angle of parallelogram ABCD.

\angle{CBX}∠CBX + \angle{ABC}∠ABC = 180°

110° + \angle{ABC}∠ABC = 180°

\angle{ABC}∠ABC = 180° - 110°

\angle{ABC}∠ABC = 70°

\angle{B}∠B = \angle{D}∠D

[ \therefore∴ Opposite angles of parallelogram are equal ]

so, \angle{D}∠D = 70°

\angle{DCB}∠DCB + \angle{ABC}∠ABC = 180°

[ \therefore∴ Supplementary angles ]

\angle{DCB}∠DCB + 70° = 180°

\angle{DCB}∠DCB = 180° - 70°

\angle{DCB}∠DCB = 110°

Now,

\angle{C}∠C = \angle{A}∠A

[ \therefore∴ Opposite angles of parallelogram are equal ]

\angle{A}∠A = 110°