Question

In the above figure O is the centre of the circle $\angle$AOB = ${80}^{\circ }$ ^,then complete the matching.
$\begin{array}{cc}Angle& Value\\ 1.ACB& a.{90}^{\circ }\\ 2.ADB& b.{40}^{\circ }\\ 3.ABC& c.{80}^{\circ }\\ 4.AOC& d.{180}^{\circ }\end{array}$

• 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 centre 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 = ${40}^{\circ }$