Question

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

Given : $\angle$ABD = 110${}^{\circ }$

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

Answer 1

The correct option is D

∠ABD = 60^o

Here $\angle$ABD and $\angle$DBC forms a linear pair, since they are adjacent to each other and lie on a straight line.
Hence, $\angle$ABC = 180${}^{\circ }$
Given $\angle$ABD = 110${}^{\circ }$
$\angle$ABC = $\angle$ABD + $\angle$ DBC
$\angle$ DBC = $\angle$ABC - $\angle$ABD
$\angle$ DBC = 180${}^{\circ }$- 110${}^{\circ }$
= 70${}^{\circ }$

$\therefore \angle$ DBC = 70${}^{\circ }$