Question

13. In the figure, if O is the centre of the circle, then the measure of x is:
(a) 40°
(b) 80
(c) 50°
(d) 110
​

Answer 1

Answer:

<aob -20 by theorem of circle

and <oab - <oba (radius equal in circle)

so 20+2x equal to 180

xequal to 80

Step-by-step explanation:

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Answer 2

Given,

In the figure,

O is the center of the circle.

The measure of angle ACB = 40°

To find,

The measure of x.

Solution,

We can simply solve this mathematical problem using the following process:

As per geometry;

In a circle, a chord subtends double the angle that it subtends at any other point on the major arc of the circle. {Statment-1}

Also, sum of all the angles of a triangle is equal to 180°. {Statment-2}

Now, according to the question;

AB is a chord of the circle. Chord AB subtends angle AOB at the center and angle ACB at a point C on the major arc of the circle.

=> angle AOB = 2 × angle ACB

{according to statment-1}

=> angle AOB = 2 × 40°

=> angle AOB = 80°

Now, according to the figure;

In the ∆AOB, sides AO = BO = radius of the circle

=> ∆AOB is an isosceles triangle

=> angle OAB = angle OBA = x° {Equation-1}

(Since angles opposite to the equal sides in an isosceles triangle are equal)

Now, according to the statement-2;

Sum of the angles in the ∆AOB = 180°

=> angle OAB + angle OBA + angle AOB = 180°

=> x° + x° + 80° = 180° {From Equation-1}

=> 2x° = 100°

=> x = 50°

Hence, the value of x is equal to 50°.