Mathematics Solutions Solutions for Class 8 Math Chapter 2 Parallel Lines And Transversal are provided here with simple step-by-step explanations. These solutions for Parallel Lines And Transversal are extremely popular among Class 8 students for Math Parallel Lines And Transversal Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate. Show Page No 8:Question 1:In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the help of the figure.  Corresponding angles. Interior alternate angles. Answer:Corresponding angles : If the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of transversal, then it is called a pair of corresponding angles. Corresponding angles Alternate interior angles : A pair of angles which are on the opposite side of the transversal and inside the given lines that are intersected by the transversal. Interior alternate angles Page No 8:Question 2:Observe the angles shown in the figure and write the following pair of angles. (1) Interior alternate angles (2) Corresponding angles (3) Interior angles Answer:(1) Alternate interior angles : A pair of angles which are on the opposite side of the transversal and inside the given lines that are intersected by the transversal.
Interior alternate angles (2) Corresponding angles : If the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of transversal, then it is called a pair of corresponding angles. Corresponding angles (3) Interior angles : A pair of angles which are on the same side of transversal and inside the given lines that are intersected by the transversal. Interior angles Page No 11:Question 1:1. Choose the correct alternative. (A) 135° (B) 90° (C) 45° (D) 40° (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° Answer:(1) Let us mark the points P and Q on m; R and S on n; A and B on p. Suppose PQ and AB intersect at M; RS and AB intersect at N. Since, m||n and p is a transversal, then m∠QMN + m∠SNM = 180° (Interior angles on the same side of transversal are supplementary) Substituing the values in the above equation, we get 3x + x = 180° ⇒ 4x = 180° ⇒ x = 180°4 ∴ x = 45° So, the correct answer is option (C). (2) Let us mark the points P and Q on a; R and S on b; A and B on l. Suppose PQ and AB intersect at M; RS and AB intersect at N. Since a||b and l is a transversal, then m∠RNM = m∠SNB (Vertically opposite angles) ⇒ ∠RNM = 2x Now, m∠RNM + m∠PMN = 180° (Interior angles on the same side of transversal are supplementary) ⇒ 2x + 4x = 180° ⇒ 6x = 180° ⇒ x = 180°6 ⇒ x = 30° So, the correct answer is option (D). Page No 11:Question 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 figure. Answer:
Let us mark the points P and Q on p; R and S on q; A and B on t; C and D on s. Suppose PQ and AB intersect at K; PQ and CD intersect at X. Suppose RS and AB intersect at L; RS and CD intersect at Y. Since, AB is a straight line and ray KQ stands on it, m∠AKX + m∠XKL = 180° (angles in linear pair) ⇒ 40° + m∠XKL = 180° ⇒ m∠XKL = 180° − 40° ⇒ m∠XKL = 140° Since, p||q and t is a transversal, then m∠YLB = m∠XKL (Corresponding angles) ⇒ x = 140° Since, RS and CD are two straight lines intersecting at Y, then m∠XYL = m∠SYD (Vertically opposite angles) ⇒ m∠XYL = 70° Since, p||q and s is a transversal, then m∠KXY + m∠XYL = 180° (Interior angles on same side of transversal are supplementary) ⇒ y + 70° = 180° ⇒ y = 180° − 70° ⇒ y = 110° Page No 12:Question 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:
Let us mark the points A and B on p; X and Y on q; P and Q on l; R and S on m. Suppose AB and XY intersect PQ at K and L respectively. Suppose AB and XY intersect RS at N and M respectively. Since, p||q and l is a transversal, then m∠AKL + m∠XLK = 180° (Interior angles on same side of transversal are supplementary) ⇒ 80° + m∠XLK = 180° ⇒ m∠XLK = 180° − 80° ⇒ m∠XLK = 100° Since, PQ and XY are straight lines that intersect at L, then m∠QLM = m∠XLK (Vertically opposite angles) ⇒ a = 100° Since, l||m and p is a transversal, then m∠BNR = m∠AKL (Alternate exterior angles) ⇒ c = 80° Since, p||q and m is a transversal, then m∠NMY= m∠RNB (Corresponding angles) ⇒ b = c ⇒ b = 80° Page No 12:Question 4:In the adjoining figure, line a ∥ line b. Line l is a transversal. Find the measures of ∠x,
∠y, ∠z using the given information. Answer:
Let us mark the points A and B on l; K and M on a; L and N on b. Suppose KM and LN intersect AB at P and Q respectively. Since, a||b and l is a transversal, then m∠PQL = m∠APK (Corresponding angles) ⇒ x = 105° Since, AB and LN are straight lines that intersect at Q, then m∠BQN = m∠PQL (Vertically opposite angles) ⇒ y = x ⇒ y = 105° Since, AB is a straight line and ray QN stands on it, then m∠BQN + m∠PQN = 180° (Angles in linear pair) ⇒ y + m∠PQN = 180° ⇒ 105° + m∠PQN = 180° ⇒ m∠PQN = 180° − 105° ⇒ m∠PQN = 75° Now, m∠APM = m∠PQN (Corresponding angles) ⇒ z = 75° Page No 12:Question 5:In the adjoining figure, line p ∥ line l ∥ line q. Find ∠x with the help of the measures given in the figure. Answer:
Let us mark the points A, L and B on p; C, M and D on l; P, N and Q on q. Since, AB||CD and LM is a transversal intersecting AB at L and CD at M, then m∠LMD = m∠ALM (Alternate interior angles) ⇒ m∠LMD = 40° Since, CD||PQ and MN is a transversal intersecting CD at M and PQ at N, then m∠DMN = m∠PNM (Alternate interior angles) ⇒ m∠DMN = 30° Now, m∠LMD + m∠DMN = 40° + 30° ⇒ m∠LMN = 70° ⇒ x = 70° Page No 13:Question 1:Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line l. Answer: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. Page No 13:Question 2:Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l. Answer: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. Page No 13:Question 3:Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from it. Answer: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. View NCERT Solutions for all chapters of Class 8 What is corresponding angle for Class 8?Answer: Corresponding angles : If the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of transversal, then it is called a pair of corresponding angles.
What are two parallel lines cut by a transversal?If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .
What are the angles formed by a transversal and parallel lines?If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
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Parallel lines and transversals worksheet pdf answer key
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