Question

in the figure, o is centre of the circle passing through P,Q,R and S. if Angle SOQ=150°, find the val
ues of x and y.

Answer 1

SOQ us 150* then x*=150/2=75*
Next, x+y=180*. Opp. Angles of cyclic quadrilateral form 180* .
75+y=180*
y=180-75=105*

Answer 2

Given:

• O is the center of the circle.

• ∠SOQ = 150°

To Find:

• The value of x and y.

Solution:

In the figure,

∠SOQ is the reflex angle and it is equal to 360°-150° = 210°

Now from the figure, we can say that,

x = (1/2)*reflex∠SOQ

x = (1/2)*210 = 105°

In the above step we divided the terms.

From the figure,

x + y = 180° {opposite angles of a cyclic quadrilateral}

Substitute the value of x in the above equation. We get,

⇒ 105° + y = 180°

⇒ y = 180°-105° {subtracting the terms}

⇒ y = 75°

∴ The value of x = 105° and y = 75°