Question

In the above figure O is the center of the circle $\angle$AOB = ${80}^{\circ }$, then match the following.

$\begin{array}{cc}Angle& Value\\ 1.ACB& a.90\\ 2.ADB& b.40\\ 3.ABC& c.80\\ 4.AOC& d.180\end{array}$

• A. a-1, b-2, c-3, d-4
• B. a-2, b-1, c-3, d-4
• C. a-4, b-3, c-2, d-1
• D. a-3, b-2, c-2, d-1

Answer 1

The correct option is C

a-4, b-3, c-2, d-1

AOC is a straight line, so $\angle$AOC should be a straight angle. Therefore $\angle$AOC = ${180}^{\circ }$.

Diameter is also a chord of the circle .The angle subtended by AC at the center is $\angle$AOC = ${180}^{\circ }$

Since angle subtended by a chord at the center is equal to twice the angle subtended by chord at any point on the circle,

We get $\angle$AOC = 2 $\angle$ABC

$\angle$ABC = ${90}^{\circ }$

Similarly, $\angle ADB=\frac{1}{2}\angle AOB$

$\angle ACB=\frac{1}{2}\angle AOB$

From the above equations we can see that $\angle ADB=\angle ACB=\frac{1}{2}\angle AOB$

$\angle$ADB = $\angle$ACB = ${40}^{\circ }$