Question

In the given figure $\angle$ AOC=${130}^{\circ }$, The value of $\angle$ ABC (in degrees) is _______.

• A. 115º
• B. ${115}^{\circ }$
• C. $50\circ$
• D. ${100}^{\circ }$

Answer 1

The correct option is B

${115}^{\circ }$

Given $\angle$AOC = ${130}^{\circ }$
To find $\angle$ABC = ?
Construction. Take a point P. anywhere on the circle. Join AP and CP. Procedure

Subtend $\angle$AOC at centre and $\angle$APC at remaining part of the circle.
$\angle$APC = $\frac{1}{2}$ $\angle$AOC ($\angle$AOC = ${130}^{\circ }$) = $\frac{1}{2}$ $\times$${130}^{\circ }$= ${65}^{\circ }$
Again, $\angle$ABC + $\angle$APC = ${180}^{\circ }$
$\angle$ABC + ${65}^{\circ }$ = ${180}^{\circ }$
$\angle$ABC = ${180}^{\circ }$- ${65}^{\circ }$ =${115}^{\circ }$