Question

Which one of the following can be an angle of a rhombus, if one of the angles is 57°?

Answer 1

ABCD is a rhombus, ∠A=50o

Opposite angles of a rhombus are equal.

∴  ∠A=∠C=50o

∴  ∠B=∠D

Sum of four angles of a rhombus is 360o.

∴  ∠A+∠B+∠C+∠D=360o

⇒  50o+∠B+50o+∠B=360o               [ Since, ∠B=∠D ]

⇒  100o+2∠B=360o

⇒  2∠B=260o

⇒  ∠B=130o

∴  ∠B=∠D=130o

We get, remaining three angles are 50o,130o,130o.