Question

In the given figure determine the value of x.

• A. ${90}^{\circ }$
• B. ${115}^{\circ }$
• C. ${130}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

Answer: (B)

${115}^{\circ }$

In the figure,

$2\times \angle ABC=reflex\angle ADC$ (Angle at the centre is twice the angle at circumference subtended by the same arc)

$=>2\times \angle ABC=({360}^o-\angle ADC)$

$=>2\times \angle ABC={360}^o-{130}^o$

$=>2\times \angle ABC={230}^o$

$=>\angle ABC=\frac{{230}^o}{2}$

$=>\angle ABC={115}^0$

$=>x={115}^0$