Question

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

• A. 95
• 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 $\angle$A0C 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 = ${180}^{\circ }$- ${65}^{\circ }$ =${115}^{\circ }$