Q6 of 9 Page 150

RENT is a rectangle. Its diagonal meet at point O. Find x if OR = 3x + 6 and OT = 5x + 2.


OE = OT = 5x + 2


[Diagonals of a rectangle bisect each other]


ON = OR = 3x + 6


[Diagonals of a rectangle bisect each other]


We also know that the diagonals of a rectangle are equal.


Therefore,


RN = ET


RN = OR + ON = 2(3x + 6) = 6x + 12


ET = OE + OT = 2(5x + 2) = 10x + 4


Now,


6x + 12 = 10x + 4


4x = 8


x = 2.


More from this chapter

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4

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is

(A) 55°


(B) 50°


(C) 40°


(D) 25°

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In a cyclic quadrilateral ABCD. ∠A= (2x+4)°, ∠B = (y+3)°, ∠C = (2y+10)°, and ∠D = (4x–5)°. Find the measure of each angle.

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Two angles of a quadrilateral measure 85° and 75° respectively. The other two angles are equal. Find the measure of each of these equal angles.

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In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5.

a) Calculate each angle of the quadrilateral.


b) Assign a special name to quadrilateral ABCD.