Question

In the figure, chords AD and BC intersect each other at right angles at a point P. If $\angle DAB={35}^o,then\angle ADC=$

• A. ${35}^o$
• B. ${45}^o$
• C. ${55}^o$
• D. ${65}^o$

Answer 1

The correct option is C

${55}^o$

Two chords AD and BC intersect each other at right angles at P and $\angle DAB={35}^o$.

In $\Delta ABP$, Ext. $\angle APC=\angle B+\angle A$

$\Rightarrow {90}^o=\angle B+{35}^o$

$\angle B={90}^o-{35}^o={55}^o$

$\because \angle ABCand\angle ADC$ are in the same segment.

$\therefore \angle ADC=\angle ABC={55}^o$