Q3 of 59 Page 73

is cyclic, ∠R = (5x - 13)°, ∠N = (4x + 4)°. Find measures of and

Given MRPN is a cyclic quadrilateral.


⇒∠ R + ∠ N = 180° {Using Opposite angles of a cyclic quadrilateral are supplementary}


⇒ (5x - 13)° + (4x + 4)° = 180°


⇒9x - 9 = 180°


⇒ x – 1 = 20°


⇒ x = 21°


∠R = (5x - 13)° = 5 × 21 – 13 = 105 – 13 = 92°


∠N = (4x + 4)° = 4 × 21 + 4 = 84 + 4 = 88°


More from this chapter

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1

In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.


(1) ∠ AOB (2) ∠ ACB


(3) arc AB (4) arc ACB.


 2

In figure 3.57, is cyclic. side PQ ≅ side RQ. ∠ PSR = 110°, Find-


(1) measure of ∠ PQR


(2) m(arc PQR)


(3) m(arc QR)


(4) measure of ∠ PRQ


4

In figure 3.58, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.


 5

Prove that, any rectangle is a cyclic quadrilateral.