# S.chand books class 8 maths solution chapter 19 Special Types of Quadrilaterals exercise 19 D

EXERCISE 19 D
1.EFGH is a rhombus. Find a , b , c

2.PQRS is a rectangle whose diagonals intersect at point O. IF OP=4x-1 and OS=2x+7. Find the value of x.

3.The diagonals of a rectangle ABCD intersect at O. If angleAOB=114 deg , find angleACD and angleADB .

4.ABCD is a rhombus with angleBDC=38deg. Find angleBCD

5.PQRS is a rhombus with angleSPR=44deg. Find anglePSQ and anglePQR.

6.(i) ABCD is a rhombus. angleBAC=37deg. Draw a sketch and find the four angles of the rhombus.
(ii) If an angle of a rhombus is 50 deg. Find the size of the angle of one of the triangles which are formed by the diagonals.

7.If the base angles of an isosceles trapezium are 56 deg each, what is the measure of the other two angles ?

8.Calculate the angles marked with small letters in the following diagrams.
(i)
(ii)
(iii)
(iv)
(v)
(vi)

9.ABCD is kite. Find the angles marked x and y in the given figures.
(i)fig
(ii) fig

10.ABCD is an isosceles trapezium and ABEF os a kite. angleFAB= 43 deg and angleAFE=137 deg . Find x and y .

11.If the diagonals of a rhombus are 12 cm and 16 cm, find the length of each side.

12.ABCD is a rhombus and its diagonals intersect at O.
(i) Is deltaAOBsimilaritydeltaBOC? State the congruence condition used.
(ii) Also, state if angleBCO=angleDCO .Deduce that each diagonal of a rhombus bisects the angles through which it passes.

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