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]

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