Rectilinear Figures Exercise 13



Q1 If two angles of a quadrilateral are 40 and 110 and the other two are in the ratio 3 : 4, find these angles.

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Q2 If the angles of a quadrilateral, taken in order, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.

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Q3 If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.

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Q4 (a) In figure (1) given below, ABCD is a parallelogram in which DAB = 70, DBC = 80. Calculate angles CDB and ADB.

(b) In figure (2) given below, ABCD is a parallelogram. Find the angles of the AAOD.

(c) In figure (3) given below, ABCD is a rhombus. Find the value of x.

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Q5 (a) In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y.

(b) In figure (2) given below. ABCD is a parallelogram. Find the values of x and y.

(c) In figure (3) given below. ABCD is a rhombus. Find x and y.

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Q6 The diagonals AC and BD of a rectangle > ABCD intersect each other at P. If ABD = 50, find DPC.

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Q7 (a) In figure (1) given below, equilateral triangle EBC surmounts square ABCD. Find angle BED represented by x.

(b) In figure (2) given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ECD = 146, find the angles of the ∆ AOB.

(c) In figure (3) given below, ABCD is rhombus and diagonals intersect at O. If OAB : OBA = 3:2, find the angles of the ∆ AOD.

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Q8 (a) In figure (1) given below, ABCD is a trapezium. Find the values of x and y.

(b) In figure (2) given below, ABCD is an isosceles trapezium. Find the values of x and.y.

(c) In figure (3) given below, ABCD is a kite and diagonals intersect at O. If DAB = 112 and DCB = 64, find ODC and OBA.

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Q9 If two angles of a quadrilateral are 40 and 110 and the other two are in the ratio 3 : 4, find these angles.

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Q10 ABCD is a parallelogram. If the diagonal AC bisects A, then prove that:

(i) AC bisects C
(ii) ABCD is a rhombus
(iii) AC ⊥ BD.

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Q11 (i) Prove that bisectors of any two adjacent angles of a parallelogram are at right angles.

(ii) Prove that bisectors of any two opposite angles of a parallelogram are parallel.

(iii) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then prove that it is a square.

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