Question

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

• A. 115º
• B. 115
• C. 50
• D. 100

Answer 1

The correct option is B

115

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 = ${180}^{\circ }$ - ${65}^{\circ }$ = ${115}^{\circ }$