Question

In circle O, AC and BD are diameters.

Answer 1

Answer:  The correct option is (C) 120°.

Step-by-step explanation:  Given that Ac and BD are the diameters of the circle with center 'O'.

We are to find the measure of arc AB.

Since AC and BD are diameters of the circle, and diameters subtends an angle of 180° at the center, so we have

$m\angle AOC=180^\circ,\\\\m\angle BOD = 180^\circ.$

From the figure, we get

$m\angle AOC=180^\circ\\\\\Rightarrow m\angle AOB+x^\circ=180^\circ\\\\\Rightarrow m\angle AOB=180^\circ-x^\circ~~~~~~~~~~~~~~~~~~(i)$

Since the diameters AC and BD intersect at the center 'O', so ∠AOC and ∠BOD are vertically opposite angles. Hence, they must be equal.

So,

$m\angle AOB=m\angle COD\\\\\Rightarrow 180^\circ-x^\circ=x^\circ+x^\circ~~~~~~~~~~~~~~~~~~~~~\textup{[using equation (i)]}\\\\\Rightarrow 3x^\circ=180^\circ\\\\\Rightarrow x^\circ=60^\circ.$

Therefore, from equation (i), we get

$m\angle AOB=180^\circ-60^\circ\\\\\Rightarrow m\angle AOB=120^\circ\\\\\Rightarrow m~\textup{arc AB}=120^\circ.$

Thus, the measure of arc AB is 120°. Option (C) is correct.

Answer 2

Because AC is a diameter we can find the 180/3 = x

giving us the x= 60

Then that arc AB = 120