Question

In a parallelogram ABCD, If $\angle DAB={75}^{\circ }$ and $\angle DBC={60}^{\circ },then\angle BDC=$

• A. ${75}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is C

${45}^{\circ }$

In || gm ABC,

$\angle A={75}^{\circ },\angle DBC={60}^{\circ }$

But $\angle A+\angle B={180}^{\circ }\text{(Sum of two consecutive angles)}\Rightarrow {75}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{75}^{\circ }={105}^{\circ }$

But $\angle DBC={60}^{\circ }$

$\therefore \angle DBA={105}^{\circ }-{60}^{\circ }={45}^{\circ }$

But $\angle BDC=\angle DBA$ (Alternate angles)

$\therefore \angle BDC={45}^{\circ }$