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Q1) External angle of a regular polygon is 72°. Find the sum of all the interior angles of it. 1) 360° 2) 720° 3) 540° 4) 648° Sides = 360°/72° = 5 Sum of all the interior angles = 5×(180 - 72) = 540° Hence, option 3. Q2) The ratio of the numbers of sides of two regular polygons is 1:2. If each interior angle of the first polygon is 120° then the measure of each interior angle of the second polygon is 1) 160° 2) 150° 3) 140° 4) 135° Number of sides of first polygon =  Number of sides of first polygon = 12 Exterior angle of second polygon = 360°/12 = 30° Interior angle of second polygon = 180° - 30° = 150° Hence, option 2. Q3) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a 1) Rectangle 2) Square 3) Rhombus 4)Trapezium As diagonals are equal and bisect each other at right angles so the quadrilateral is a square. Hence, option 2. Read More: Important Properties of PolygonsQ4) A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC=BD, then the quadrilateral must be a1) Trapezium 2) Parallelogram 3) Rhombus 4) None of these Quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel is a trapezium. Hence, option 1. Q5) Let X be any point within a square ABCD. On AX, a square AXYZ is described such that D is within it. Which one of the following is correct? 1) AX = DZ 2) ∠ADZ = ∠BAX 3) AD = DZ 4) BX = DZ In ∆ ABX and ∆ ACZ AB = AD (Side of square ABCD) AX = AZ (Side of a square AXYZ) ∠BAX = θ; ∠XAD = 90° - θ As AXYZ is a square. ∠ZAX = 90° ∠ZAD + ∠XAD = 90° ZAD = 90° - (90° - θ) = θ ∠BAX = ∠ZAD ∆ ABX≅∆ ADZ BX = DZ Hence, option 4. Q6) Consider the following statements: A) The perpendicular bisector of a chord of a circle does not pass through the center of the circle. B) The angle in a semi-circle is a right angle. Which of the statements given above is/are correct. 1) Only A 2) Only B 3) Both A and B 4) Neither A nor B The perpendicular bisector of a chord of a circle always pass through the center. So, statement A is wrong. Statement B is correct. Hence, option 2. Q7) Each of the two circles of same radius a pass through the center of the other. If the circles cut each other at the points A, B and O, O’ be their centers, then the area of the quadrilateral AOBO’ is 1) a2/4 2) a2/2 3) 0.866a2 4) a2 Area of quadrilateral AOBO’ = Area of ∆ AOO' + Area of ∆ BOO' AO = OO' = AO' = a So, AOO’ is an equilateral triangle. Similarly, BOO’ is an equilateral triangle. Area of quadrilateral AOBO’ is  Hence, option 3. Q8) A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC=BD, then the quadrilateral must be a 1) Trapezium 2) Parallelogram 3) Rhombus 4) None of these Quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel is a trapezium. Hence, option 1. |