Question

in the following figure if o is the centre of the circle and angle acb = 50 degree then find xCD​

Answer 1

The measure of an angle ∠ OAB is 40°.

Step-by-step explanation:

Given:

∠ACB = 50°

O is the center of Circle

To Find:

∠ OAB = ?

Solution:

Angle Inscribe Theorem:

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

∴ center angle, ∠ AOB = 2 × ∠ ACB

Substituting we get

$\angle AOB =2\times 50=100\°$

Now, In ΔAOB

$AO = BO$........Radius of same circle

∴ ΔAOB is an Isosceles Triangle

∴ ∠OAB = ∠OBA ........Isosceles Triangle Property

Now, In ΔAOB

$\angle AOB+\angle OAB+\angle OBA =180$.....Triangle Sum Property

Substituting we get

$2m\angle OAB=180-100=80\\\\m\angle OAB=\dfrac{80}{2}=40\°$

The measure of an angle ∠OAB is 40°