Question

In the given figure, ABCD is a rhombus. Diagonals AC and BD intersect each other at E. $\angle 1={50}^o$ then $\angle BCD=$

• A. ${100}^o$
• B. ${90}^o$
• C. ${80}^o$
• D. none of these

Answer 1

The correct option is C ${80}^o$

ABCD is a rhombus. Diagonals AC and BD intersect each other at E.
Given, $\angle 1={50}^o$
BD bisects $\angle ABC$ ( by property of rhombus)
So, $\angle ABC=2\times {50}^o={100}^o$
$\angle ABC+\angle BCD={180}^o$ ----(Interior angles on the same side of transversal)
$\angle BCD={180}^o-\angle ABC={180}^o-{100}^o={80}^o$