class 8 : maths :Parallel lines and transversals : All Practice set

 class 8 : maths :Parallel lines and transversals : Practice set 2.1QUE 1. In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the
help of the figure.
Corresponding angles.Corresponding angles:i. ∠p and __ii. ∠q and __iii. ∠r and __iv. ∠s and __Interior alternate angles:v. ∠s and __vi. ∠w and __ANSWER :i. ∠wii. ∠xiii. ∠yiv. ∠zv. ∠xvi. ∠rQUE 2. Observe the angles shown in the
figure and write the following pair of
angles(1) Interior alternate angles  (2) Corresponding angles  (3) Interior anglesANSWER :∠c and ∠e; ∠b and ∠h∠a and ∠e; ∠b and ∠f; ∠c and ∠g; ∠d and ∠h∠c and ∠h; ∠b and ∠e class 8 : maths :Parallel lines and transversals : Practice set 2.21. Choose the correct alternative.  (1) In the adjoining figure, if line m || line n and line p is a transversal then find x.  (A) 135° (B) 90° (C) 45° (D) 40° Solution:(C) 45°ANSWER :line m || line n and line p is a transversal.∴ m∠BFG + m∠FGD = 180°…[Interior angles]∴ 3x + x = 180°∴ 4x = 180°∴ x = 1804∴ x = 45°(2) In the adjoining figure, if line a || line b and line l is a transversal then find x.  (A) 90° (B) 60° (C) 45° (D) 30°Solution:(D) 30°ANSWER :line a || line b and line l is a transversal.∴ m∠UVS = m∠PUV…[Alternate angles]= 4xm∠UVS + m∠WVS = 180°… [Angles in a linear pair]∴ 4x + 2x = 180°∴ 6x = 180°∴ x = 1806∴ x = 30°2. In the adjoining figure line p ||  line q. Line t and line s are transversals. Find measure of ∠x and ∠ y using the measures of angles given in the figureANSWER :i. Consider ∠z as shown in figure.line p || line q and line t is a transversal.∴ m∠z = 40° …(i) [Corresponding angles]m∠x + m∠z = 180° …[Angles in a linear pair]∴ m∠x + 40o = 180° …[From(i)]∴ m∠x= 180° – 40°∴ m∠x = 140°ii. Consider ∠w as shown in the figure.m∠w + 70° = 180° …[Angles in a linear pair]∴ m∠w = 180° – 70°∴ m∠w = 110° …(ii)line p || line q and line s is a transversal.∴ m∠y = m∠w …[Alternate angles]∴ m∠y =110° …[From (ii)]∴ m∠x = 140°, m∠y = 110°3. In the adjoining figure. line p || line q. line l || line m. Find measures of ∠a, ∠b, and ∠c, using the measures of given angles. Justify your answers.ANSWER :Solution:i. line p || line q and line l is a transversal.∴ m∠a + 80° = 180° …[Interior angles]∴ m∠a= 180° – 80°∴ m∠a= 100°ii. line l || line m and line p is a transversal.∴ m∠c = 80° …(i) [Exterior alternate angles]iii. line p || line q and line m is a transversal.∴ m∠b = m∠c … [Corresponding angles]m∠b = 80° …[From (i)]∴ m∠a = 100°, m∠b = 80°, m∠c = 80°4. In the adjoining figure, line a || line b. line l is a transversal. Find the measures of  ∠x, ∠ y, ∠z using the given informationANSWER :line a || line b and line l is a transversal.∴ m∠x = 105° …(i) [Corresponding angles]ii. m∠y = m∠x … [Vertically opposite angles]∴ m∠y = 105° …[From (i)]iii. m∠z + 105° = 180° …[Angles in a linear pair]∴ m∠z = 180°- 105°∴ m∠z = 75°∴ m∠x = 105°, m∠y = 105°, m∠z = 75°5. In the adjoining figure, line p || line l || line q. Find ∠ x with the help of the measures given in the figure.ANSWER :line p || line l and line IJ is a transversal.m∠IJN = m∠JIH … [Alternate angles]∴ m∠IJN = 40° …(i)line l || line q and line MJ is a transversal.m∠MJN = m∠JMK … [Alternate angles]∴ m∠MJN = 30° …(ii)Now, m∠x = m∠IJN + m∠MJN…[Angle addition property]= 40° + 30° …[From (i) and (ii)]∴ m∠x = 70° class 8 : maths :Parallel lines and transversals :Practice set 2.31. Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line lANSWER :Steps of construction :(1) Draw a line l. Take a point A outside the line l.(2) Draw a segment AM ⊥ line l.(3) Take another point N on line l.(4) Draw a segment NB ⊥ line l, such that l(NB) = l(MA).(5) Draw a line m passing through the points A and B.Hence, the line m is the required line that passes through point A and parallel to line l.2. Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line lANSWER :Steps of construction :(1) Draw a line l. Take a point T outside the line l.(2) Draw a segment MT ⊥ line l.(3) Take another point N on line l.(4) Draw a segment NV ⊥ line l, such that l(NV) = l(MT).(5) Draw a line m passing through the points T and V.Hence, the line m is the required line that passes through point T and parallel to line l.3. Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from itANSWER :Steps of construction :(1) Draw a line m.(2) Take two points A and B on the line m.(3) Draw perpendiculars to the line m at A and B.(4) On the perpendicular lines, take points P and Q at a distance of 4 cm from A and B respectively.(5) Draw a line n passing through the points P and Q.So, line n is the required line parallel to the line m at a distance of 4 cm away from it.