Question

Measure of one angle of a rhombus is ${50}^o$, find the measures of remaining three angles.

Answer 1

$ABCD$ is a rhombus, $\angle A={50}^o$

Opposite angles of a rhombus are equal.

$\therefore$ $\angle A=\angle C={50}^o$

$\therefore$ $\angle B=\angle D$

Sum of four angles of a rhombus is ${360}^o.$

$\therefore$ $\angle A+\angle B+\angle C+\angle D={360}^o$

$\Rightarrow$ ${50}^o+\angle B+{50}^o+\angle B={360}^o$ [ Since, $\angle B=\angle D$ ]

$\Rightarrow$ ${100}^o+2\angle B={360}^o$

$\Rightarrow$ $2\angle B={260}^o$

$\Rightarrow$ $\angle B={130}^o$

$\therefore$ $\angle B=\angle D={130}^o$

We get, remaining three angles are ${50}^o,{130}^o,{130}^o.$