Question

Question 7
In the figure, if $\angle DAB={60}^{\circ },\angle ABD={50}^{\circ }$ then $\angle ABC$ is equal to

(A) ${60}^{\circ }$
(B) ${50}^{\circ }$
(C) ${70}^{\circ }$
(D) ${80}^{\circ }$

Answer 1

(C) ${70}^{\circ }$

$Given,\angle DAB={60}^{\circ },\angle ABD={50}^{\circ }$
$Since,\angle ADB=\angle ACB$.......(i) [angles in same segment of a circle are equal]

$In\Delta ABD,\angle ABD+\angle ADB+\angle DAB={180}^{\circ }$ [by angle sum property of triangle]
$\therefore {50}^{\circ }+\angle ADB+{60}^{\circ }={180}^{\circ }$
$\Rightarrow \angle ADB={180}^{\circ }-{110}^{\circ }={70}^{\circ }$
$FromEq.\left(i\right),\angle ACB=\angle ADB={70}^{\circ }$