Question

Which of the following statements are true about the figure given below?

• A. ∠DBC = 180^o
• B. ∠CBA = 90^o
• C. ∠CBA and ∠DBA are supplementary.
• D. ∠ABD = 60^o

Answer 1

Answer: (A), (B), (C)

The correct options are
A

∠DBC = 180^o

B

∠CBA = 90^o

C

∠CBA and ∠DBA are supplementary.

Here $\angle$ABD and $\angle$ABC are supplementary, since they lie on a straight line.
Hence $\angle$DBC = 180${}^{\circ }$
As shown, $\angle$ABC = 90${}^{\circ }$
$\therefore \angle$ ABD = 180 - $\angle$ ABC = 180 - 90 = 90${}^{\circ }$