### Download: PDF e-books for Aptitude

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 a1) Rectangle 2) Square 3) Rhombus4)TrapeziumAs 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) Rhombus4) None of theseQuadrilateral 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 = DZ4) BX = DZIn ∆ 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 B3) Both A and B4) Neither A nor BThe 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’ is1) a^{2}/4 2) a^{2}/2 3) 0.866a^{2}4) a^{2} 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 a1) Trapezium 2) Parallelogram 3) Rhombus4) None of theseQuadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel is a trapezium. Hence, option 1. |