ID : gb-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) If you divide a circle into 9 equal parts by drawing radii, then what is the angle between any two adjacent radii so drawn (2) What is the minimum number of line segments that can be used to create a closed f igure? (3) If an angle is 1 of its supplementary angle, then what is the value of that angle? (4) What is a polygon with 4 sides is called? Choose correct answer(s) f rom given choice (5) NOTE: Assume that the value of "pi" (ratio of the circle's circumf erence to diameter) is 3. If the radius of a circle is 85.6 cm then what is the circumf erence of that circle? a. 684.8 cm b. 171.2 cm c. 256.8 cm d. 513.6 cm (6) How many circles can be drawn with a given center? a. 986 b. unlimited c. 2 d. 1 (7) What kind of angle is described by the f ollowing f igure a. Obtuse angle b. Right angle c. Straight angle d. Acute angle (8) If you were to bisect (or divide into half ) an obtuse angle, the divided angles would be a. obtuse angles b. complementary angles c. right angles d. acute angles
ID : gb-5-geometry [2] Fill in the blanks (10) If the radius of a circle is 61.8 dm then the diameter is dm. () It is not possible f or an angle and its supplementary angle to be part of a triangle - (T/F) (12) A diameter divides a circle in equal parts. (13) If angle ADC and BDC are right angle, value of x + y =. (14) Concentric circles are the circles having the same. (15) The value of the supplement of the complement of 6 is 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : gb-5-geometry [3] (1) 40 (2) Three (A triangle is the f igure that can be thus generated) A line segment is part of a line that is bounded by two distinct end points, and contains every point on the line between its end points. One line segment can not be used to create a closed f igure. Two line segments also can not be used to create a closed f igure as shown below: Three line segment can be used to create a closed f igure. For example, a triangle has three line segments and f orms a closed f igure. Theref ore, three is the minimum number of line segments required to create a closed f igure.
(3) 15 ID : gb-5-geometry [4] It is given that the angle is 1 of its supplementary angle. T heref ore, the sum of this angle and its supplementary angle will be, 1 + 1 = 12 times the supplementary angle. We know that the sum of an angle and its supplementary angle is 180. 12 times supplementary angle = 180 Theref ore, the supplementary angle = 180 12 Supplementary angle = 165 Theref ore, the required angle = 180-165 = 15 (In higher grades you will learn Algebra, using which such questions can be solved very easily. For more details read this article. Algebra A f ascinating subject) (4) Quadrilateral (5) d. 513.6 cm (6) b. unlimited (7) d. Acute angle In the given f igure, B = 50 which is greater than 0 but less than 90. In other words: 0 < 50 < 90 An angle whose measure is more than 0 but less than 90 is called Acute angle. Hence B is an Acute angle.
(8) d. acute angles ID : gb-5-geometry [5] An obtuse angle is one whose measure is more than 90 but less than 180. If an obtuse angle is bisected (or divided into half ), then each angle will be more than 45 and less than 90. All such angles will be acute angles since an acute angle is one whose measure is more than 0 but less than 90. Hence, the divided angles would be acute angles. (9) c. 78 We know that complete circumf erence of circle covers angle of 360 It is given that worm covers 360 in 1:18:00 hours. 1:18:00 hours = 4680 seconds Since in 4680 seconds, it covers angle of 360 T heref ore angle covered in 1014 seconds = 1014(360/4680) angle = 78 (10) 123.6
() T ID : gb-5-geometry [6] Let us f irst recall the f act that the sum of all three angles of a triangle is 180 degrees. Let us now look at the def inition of supplementary angles: two angles are called supplementary if the sum of their measures is 180 degrees. We need to f ind if we can have a triangle which has a pair of supplementary angles. For a moment, let us assume that such a triangle could exist. In such a triangle, the sum of two angles (supplimentary ones) will be 180 degrees. T his means that the third angles will need to be zero degrees. We know that we can not create a triangle with one of the angles being zero degrees. Step 5 This means, it is not possible f or an angle and its supplementary angle to be part of a triangle. (12) (13) two 105 We know that sum of all internal angles of a triangle is 180, theref ore f or triangle ΔADC, CAD + ADC + ACD = 180 x + 90 + 35 = 180 Theref ore x = 180-90 - 35, x = 55 Similarly in ΔCDB, y can be calculated as y = 180-90 - 40, y = 50 Theref ore, x + y = 55 + 50 x + y = 105 (14) center
(15) 96 ID : gb-5-geometry [7] If you look at the question caref ully, you will notice that f irst of all we have to f ind the complement of 6, then f ind the supplement of the complement of 6. T he sum of the complementary angles is 90. Theref ore the complement of 6 = 90-6 = 84 T he sum of supplementary angles is 180. Theref ore, the supplement of 84 = 180-84 = 96 Theref ore the value of the supplement of the complement of 6 is 96.