Question

\(\text{(D) In the given figure, O is the centre of the arc ABC which subtends an angle of} 130^\circ~ \text{at the centre.}\text{If AB is extended to P then}~\angle PBC = ___\)

• A. ${60}^{\circ }$
• B. ${100}^{\circ }$
• C. ${90}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is D

${130}^{\circ }$

Given, $\angle ADC={130}^{\circ }$

As ABCD is a cyclic quadrilateral

$\therefore$ $\angle ADC+\angle ABC={180}^{\circ }$

$\Rightarrow$ (\angle ABC~=~180-130 = 50^{\circ}\)

Now, $\angle PBC+\angle ABC={180}^{\circ }$ ($because$ angle in a straightline = ${180}^{\circ }$)

$\therefore$ (\angle PBC~=~180-50 = 130^{\circ}\)