ID : ww-6-geometry [1] Grade 6 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and CD are parallel, f ind the value of angle x. Choose correct answer(s) f rom given choice (2) If lines XY and MN intersects as shown below and a:b = 1:2, f ind c. a. 120 b. 125 c. 129 d. 114 (3) Find value of angle x a. 60 b. 30 c. 50 d. 40
(4) If AB and CD are parallel, f ind the value of angle x. ID : ww-6-geometry [2] a. 75 b. 95 c. 105 d. 115 (5) What is the angle between minute and hour hands, when clock shows 6:00 o'clock? a. 210 b. 190 c. 180 d. 170 (6) In a clock, how many right angles does a minute-hand move f rom 6:45 O'clock to 8:15 O'clock? a. 4 b. 7 c. 8 d. 6 (7) If AB and CD are parallel, f ind the value of angle x. a. 110 b. 100 c. 120 d. 70 (8) How many angles are f ormed in this picture? a. 6 b. 8 c. 10 d. 4
(9) ID : ww-6-geometry [3] Find the value of x. a. 270 b. 80 c. 90 d. 100 Fill in the blanks (10) If AC and EF are parallel, ADB = (11) If OD is perpendicular to AB, and DOC = 30, ( BOC - AOC). =. (12) If AB and CD are parallel, value of angle x is.
ID : ww-6-geometry [4] (13) If AB and DE are parallel to each other, the value of angle BCD =. (14) A ship is sailing in West direction. If it changes direction to South, the ship turns through an angle of (15) If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 4:5, then the smaller of the two angles =. 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ww-6-geometry [5] (1) 100 It is given that line AB and CD and parallel lines and the third line (say EF) cuts them as shown in the f igure. a = c (vertically opposite angles) c = e (alternate interior angles) Theref ore we can write, a = c = e = g Again, b = d (vertically opposite angles) d = f (alternate interior angles) Theref ore we can write, b = d = f = h We know that sum of two adjacent angle is equal to 180. Theref ore, f rom the diagram, you can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Given, e = 80 and b = x and e + f = 180 80 + f = 180 f = 180-80 f = 100 As f is equal to b So, x is 100. Theref ore, the value of x is 100. (2) a. 120
(3) d. 40 ID : ww-6-geometry [6] If you look at the f igure caref ully, you will notice that line AB is a straight line. The angles of straight line add up to 180. Line AB is a straight line, theref ore x + 70 + 70 = 180 140 + x = 180 x = 180-140 x = 40. Theref ore the value of angle x is 40.
(4) c. 105 ID : ww-6-geometry [7] It is given that line AB and CD and parallel lines and the third line (say EF) cuts them as shown in the f igure. a = c (vertically opposite angles) c = e (alternate interior angles) Theref ore we can write, a = c = e = g Again, b = d (vertically opposite angles) d = f (alternate interior angles) Theref ore we can write, b = d = f = h We know that sum of two adjacent angle is equal to 180. Theref ore, f rom the diagram, you can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Given, d = 105 and f = x As d is equal to f, x is 105. Theref ore, the value of x is 105.
(5) c. 180 ID : ww-6-geometry [8] At 6:00 o'clock, hour hand of the clock will be at 6 and minute hand will be at 12. In clock a whole circle is divided into 12 parts, where each part represents an hour. T heref ore, angle between consecutive numbers on clock, = 360 /12 = 30 At 12 o'clock the angle between minute and hour hands is 0 and the angle increases by 30 till 6 o'clock f or every hour. Af ter 6 o'clock the angle decreases by 30 f or every hour. Step 4 Theref ore the angle between minute and hour hands, when clock shows 6:00 o'clock = 30 6 = 180 (6) d. 6 If you read the question caref ully, you will notice that the dif f erence of time f rom 6:45 O'clock to 8:15 O'clock is 1 hour 15 minutes. Since we know that 1 hour = 60 minutes. and 1 hour = 1 60 = 60 minutes. theref ore 1 hour 15 minutes = 60 + 15 = 75 minutes. Since number of right angles made by a minute-hand in 60 minutes(1 hour) = 4 right angles number of right angles made by a minute-hand in 1 minutes = number of right angles made by a minute-hand in 75 minutes = angles 4 60 4 60 right angles 75 = 6 right Theref ore we can say that the number of right angles made by a minute-hand move f rom 6:45 O'clock to 8:15 O'clock are 6.
(7) a. 110 ID : ww-6-geometry [9] It is given that line AB and CD and parallel lines and the third line (say EF) cuts the lines AB and CD at certain angle as shown in the f igure above. Let us redraw the f igure as below: a = c (vertically opposite angles) c = e (alternate interior angles) Theref ore we can write, a = c = e = g Again, b = d (vertically opposite angles) d = f (alternate interior angles) Theref ore we can write, b = d = f = h We know that sum of two adjacent angle is equal to 180. Theref ore, f rom the diagram, you can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Here, b = 110 and h = x As b is equal to h, x is 110. Theref ore, the value of x is 110.
(8) b. 8 ID : ww-6-geometry [10] An angle is the space between two intersecting lines at or close to the point where they meet. If you look the picture caref ully you will notice that 8 angles are f ormed in this picture. Angles are ABC, BAC, ACB, ACD, ADC, CAD, DAB, DCB. (9) c. 90 If you look at the f igure caref ully, you will notice that angles 1x, 90 and 2x are made around a point. The sum of all the angles around a point is 360. theref ore 1x + 90 + 2x = 360 3x + 90 = 360 3x = 360-90 3x = 270 x = 270 3 x = 90 Now the value of x is 90.
(10) 105 ID : ww-6-geometry [11] If you look at the f igure caref ully, you will notice that ADE = 30 and DBC = 135. According to question AC and EF are parallel. Theref ore we can say that EDB and DBC are alternate interior angles. Now EDB = DBC [Alternate interior angles] ADE + ADB = DBC [Since EDB = ADE + ADB] ADB = 135 - ADE [Since ADB = 135 ] ADB = 135-30 [Since ADE = 30 ] ADB = 105 Step 4 Theref ore ADB = 105 (11) 60 According to question DOC = 30 and OD is perpendicular to AB. Theref ore AOD = 90 and BOD = 90. DOC + AOC = AOD 30 + AOC = 90 [Since AOD = 90 and DOC = 30 ] AOC = 90-30 AOC = 60 Now BOC - AOC = BOD + DOC - AOC [Since BOC = BOD + DOC] = 90 + 30-60 [Since BOD = 90, DOC = 30 and AOC = 60 ] = 60 Step 4 Theref ore BOC - AOC = 60
(12) 80 ID : ww-6-geometry [12] It is given that line AB and CD and parallel lines and the third line (say EF) cuts the lines AB and CD at certain angle as shown in the f igure above. Let us redraw the f igure as below: a = c (vertically opposite angles) c = e (alternate interior angles) Theref ore we can write, a = c = e = g Again, b = d (vertically opposite angles) d = f (alternate interior angles) Theref ore we can write, b = d = f = h We know that sum of two adjacent angle is equal to 180. Theref ore, f rom the diagram, you can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Here, h = 100 and c = x h + g = 180 100 + g = 180 g = 180-100 g = 80 As g is equal to c, x is 80. Theref ore, the value of x is 80.
ID : ww-6-geometry [13]
(14) 90 ID : ww-6-geometry [14] According to the question, the direction of ship is West. Now the direction of the ship changes to South. The angle at which the ship has to turn is actually the angle between West and South directions. Step 4 Let us look at the directions as shown below: Step 5 The angle between the West and South is 90. Step 6 Thus, the angle at which the ship has to turn f rom West to South is 90.
(15) 80 ID : ww-6-geometry [15] Let us assume that x be the f irst interior angle on the same side of a transversal intersecting two parallel lines. We know that the sum of two interior angles on the same side of a transversal intersecting two parallel lines is 180. T hus, the second interior angle on the same side of a transversal intersecting two parallel lines = 180 - x The ratio of the two interior angles on the same side of a transversal intersecting two x parallel lines = 180 - x It is given that the ratio of the two interior angles on the same side of a transversal intersecting two parallel lines = 4:5 x Theref ore, = 4 180 - x 5 By cross multiplying both sides 5x = 4(180 - x) 5x = 4 180-4x 5x + 4x = 720 9x = 720 x = 720 9 x = 80 Step 4 The f irst angle = 80 The second angle = 180-80 = 100
Step 5 ID : ww-6-geometry [16] Thus, the smaller of the two angles is = 80