Q3 of 63 Page 156

In figure, find all the four angles of the cyclic quadrilateral ABCD.

We know that the pair of opposite angles of a cyclic quadrilateral is supplementary i.e. sum is 180°.


Firstly, 2x° + 3x° = 180°


⇒ 5x° = 180°


⇒x° = 180°/ 5


∴ x° = 36°


Also, y° + 2y° = 180°


⇒ 3y° = 180°


⇒y° = 180°/ 3


∴ y° = 60°


Now,


∴ ∠A = y° = 60°


∴ ∠B = 3x° = 3 (36°) = 108°


∴ ∠C = 2y° = 2 (60°) = 120°


∴ ∠D = 2x° = 2 (36°) = 72°


More from this chapter

All 63 →
1

One angle of a cyclic quadrilateral is given. Find the opposite angle.

(i) 70° (ii) 135°


(iii) (iv) right angle


(iv) 165°

2

Find the opposite angle of a cyclic quadrilateral of one angel of these in

(i) of other


(ii) of other

 4

In figure, some angles have been marked with a, b, c and d. Find the measures of these angles.

 5

If in a cyclic quadrilateral ABCD, AD || BC, then prove that ∠A = ∠D.