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EI 16) iT angles A, B, C and D of tha, , Answer: a, , Explanation: Draw a, AB produced at EF, , line through C Parallel to DA intersecting, CE = AD (Opposite Sides), , AD = BC (Given), , BC=CE, , = ZCBE = zCEB, , also,, , ZA + ZCBE = 180° (Angles on the same side of transversal, and ZCBE = zCEB), , 2B + ZCBE = 180° ( As Linear pair), , => ZA=2zB, , 11) Which of the following is not true for a parallelogram?, (a) Opposite sides are equal, , (6) Opposite angles are equal, , (Cc) Opposite angles are bisected by the diagonals, , (d) Diagonals bisect each other, , Answer: c, , Explanation: Opposite angles are bisected by the diagonals is, not true for a parallelogram. Whereas opposite sides are, equal, opposite angles are equals, diagonals bisect each other, are the properties of a parallelogram., , 12) Three angles of a quadrilateral are 75°, 90° and 75°. The, fourth angle is, , (a) 90°, (b) 95°, (c) 105°, (d) 120°, Answer: d, , Explanation: We know that the sum of angles of a quadrilateral, is 360°., , Let the unknown angle be x., Therefore, 75°+90°+75°+x = 360°, x = 360° — 240° = 120°., , 13) ABCD is a rhombus such that 2ACB = 40°. Then zADB, is, , (a) 40°, (b) 45°, (c) 50°, (d) 60°, Answer: ¢, , Explanation: We know that the diagonals of the rhombus bisect, each other perpendicularly., , — Se, , eben dn nk oR Por, , er., , eee * eS, , 19) If APB and CQD are two parallel lines, th, , , , IP and, , of riage cone ieror angles, and angle sum property, , From the triangle, BOC,, , BOC + ZOCB + ZOBC = 180°, , (where zBOC= 90°, zOCB = 40°), , 90°+40°+ OBC = 180°, , ZOBC = 180° — 130° PQ,, ZOBC = 50° irila, ZOBC =zDBC, , Now, by using alternate angles, we can say, , ZADB = 50°, , 14) The quadrilateral formed by joining the mid-points of, , the sides of a quadrilateral PQRS, taken in order, is a, , rhombus, if, , (a) PQRS is a rhombus, , (b) PQRS is a parallelogram, , (c) Diagonals of PQRS are perpendicular, , (d) Diagonals of PQRS are equal. P, Answer: d nd, , Explanation: The quadrilateral formed by joining the mid-points AL, , of the sides of a quadrilateral PQRS, taken in order, is a, rhombus if the diagonals of PQRS are equal., , 15) A diagonal of a rectangle is inclined to one side of the, rectangle at 25°. The acute angle between the diagonals is, , (a) 25°, (b) 40°, , (c) 50°, , (d) 55°, , Answer: c, , Explanation: Consider the rectangle ABCD, , <1, Es a, , In a triangle BOC,, ZOBC = ZOCB (Opposite angles of isosceles triangle), , B, , Therefore, ZOBC + ZOCB+zBOC = 180°, 25°+25° + ZBOC = 180°, , ZBOC = 180°- 50°, , ZBOC = 130°., , By using the linear pair,, , -Oee.O3.19 12:45, , eo LLL