Q2 of 12 Page 115

The opposite angles of a cyclic quadrilateral are x and 3x. What are the measures of the angles of this quadrilateral?

As we know that


Sum of Opposite angles of cyclic quadrilateral are supplementary


If the opposite angles are x & 3x


∴ x + 3x = 180°


∴ 4x = 180°


∴ x =


∴ x = 45°


⇒ 3x = 3*45° = 135°


Hence the angles are


More from this chapter

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2

Draw a circle. Mark an arc LMN on this circle. Inscribe an angle LMN in it.

How many more angles can you inscribe in this arc?


 1

The measure of a central angle is 120°. Find the measure of the arc it intercepts.

 2

In the figure, arc AXB is a semicircle. m∠PAB = 40°. Hence, find the values of

(1) m∠APB,


(2) m(arc PYB),


(3) m(arc AZP),


 1

In the figure, m∠B = 85° and m∠C = 105°, then find the measures of ∠A and ∠D.