Grade 7 Lines and Angles Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Observe the Figure and Answer the Following Question

Illustration 2 for 1_Observe_the_figure_and_answer …

(a) Write any four pair of corresponding angles.

(b) Write any four pair of alternate interior angles.

(c) Write any four pair of co-interior angles.

(2) Find the Following Angles

(a)

Illustration 3 for 2_Find_the_following_angles

(3) Find the Following Angles

(a)

Find following angles

Illustration 4 for 3_Find_the_following_angles

(4) Find the Following Angles

(a)

Find following angles

Illustration 5 for 4_Find_the_following_angles

(5) Find the Measure of the Unknown Angles

(a) EC

Illustration 6 for 5_Find_the_measure_of_the_unknown_angles

(6) Find the Measure of Unknown Angles

(a)

Illustration 7 for 6_Find_the_measure_of_unknown_angles

(7) Find the Measure of Unknown Angles

(a)

Illustration 8 for 7_Find_the_measure_of_unknown_angles

(8) Find the Value of X

Illustration 9 for 8_Find_the_value_of_x

(9) Find the Value of Y

(a)

Illustration 10 for 9_Find_the_value_of_y

(10) Find the Value of X and Y

Illustration 11 for 10_Find_the_value_of_x_and_y

(11) Find the Value of X and Y

Illustration 12 for 11_Find_the_value_of_x_and_y

(12) Find the Value of X

(a) If Angle ∠ CAB is twice the angle ∠ PBN than find the value of x.

Illustration 13 for 12_Find_the_value_of_x

Answers and Explanations

Answer 1 (A)

  • Corresponding angle: When two lines are crossed by transversal line, the angle in matching corner are called corresponding angles.
  • Transversal line is a line that cross at least two other lines.
  • From give given figure XY and EF are transversal line for AB and CD.
  • Therefore Corresponding Angles are;

Illustration 14 for Answers_and_Explanations

Answer 1 (B)

Alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite side of the transversal line.

From figure alternate interior angles are:

Illustration 15 for Answers_and_Explanations

Answer 1 (C)

  • The pairs of angles on one side of the transversal line but inside the two lines are called consecutive interior angles.
  • From given figure following are the consecutive interior angles:

Illustration 16 for Answers_and_Explanations

Answer 2 (A)

  • From figure given.
  • Now from figure corresponding angle to given angle is angle
  • For corresponding angle when transversal line cross two parallel line than corresponding angle have same value.
  • Here given that line means AB and CD lines are parallel so that corresponding angle and have same value.

  • Now, ∠ CFQ and ∠ FQD are on same line.
  • Therefore;

Answer 3 (A)

  • For ∠ UFE:
  • Given that Line means line QR and line PS are parallel so in this case line AB act as a transversal line.
  • Therefore angle ∠ TEF and ∠ UFB are corresponding angle.
  • As, Line

  • Now angle ∠ UFB and ∠ UFE are on same line:

  • For ∠ SUD:
  • Given that Line means line AB and line CD are parallel so in this case line PS act as a transversal line.
  • Therefore angle ∠ UFB and ∠ SUD are corresponding angle.
  • As, Line

  • For ∠ ETU
  • Given that Line means line AB and line CD are parallel so in this case line QR act as a transversal line.
  • Therefore angle ∠ TEF and ∠ RTU are corresponding angle.
  • As, Line

  • Now angle ∠ RTU and ∠ ETU are on same line:

  • For ∠ AEQ:
  • Angle ∠ AEQ and ∠ TEF are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

  • For ∠ PFB:
  • Given that Line means line QR and line PS are parallel so in this case line AB act as a transversal line.
  • Therefore angle ∠ AEQ and ∠ PFB are corresponding angle.
  • As, Line

Answer 4 (A)

  • Given that Line means line AB and line CD are parallel so in this case line QR act as a transversal line.
  • Therefore angle ∠ QLA and ∠ LTC are corresponding angle.
  • As, Line

  • Given that Line means line AB and line CD are parallel so in this case line PS act as a transversal line.
  • Therefore angle ∠ PNB and ∠ NTD are corresponding angle.
  • As, Line

  • Now ∠ LTC , ∠ LTN and ∠ NTD are on same line;

  • Angle ∠ LTN and ∠ STR are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

Answer 5 (A)

  • Given that Line means line EC and line AB are parallel so in this case line BD act as a transversal line.
  • Therefore angle ∠ n and ∠ AMC are corresponding angle.
  • As, Line

  • Now Angle ∠ n and angle ∠ p are on same line

  • Now for quadrilateral ABCE

  • Given that Line means line AB and line CD are parallel so in this case line AF act as a transversal line.
  • Therefore angle ∠ m and ∠ o are corresponding angle.
  • As, Line

Answer 6 (A)

  • From figure and given data it՚s clear that and line AB is transversal line.
  • Therefore from figure angle ∠ BKG and ∠ JLC are corresponding angle
  • As, lines

  • Now angle ∠ JLC and ∠ JLO are on same line
  • Therefore

Answer 7 (A)

  • As shown in below figure if we extend the line NM than it cross the line CD at point O and form a triangle △PMO.
Illustration 17 for Answers_and_Explanations
  • As line and angle means line MN is right angle to line AB.
  • As Line AB and line CD are parallel extended line of MN will be perpendicular to line CD where it cross the line CD.
  • Therefore Angle
  • Now for triangle △PMO

  • Now angle ∠ PMO and ∠ x are on same line; therefore

Answer 8 (A)

  • From figure ∠ JKP and ∠ JKL lines on same line,

  • Now, Angle ∠ RLS and ∠ JLK are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

  • Now, for triangle △JLK

Answer 9 (A)

  • Give that Line
  • From figure line DE is transverse line.
  • So Angle ∠ ADE and ∠ DEB are Alternate interior angle. And for alternate interior angle if transverse line cross two parallel line alternate interior angle have a same value,
  • Here

  • Therefore

  • Now from figure angle ∠ ACE and ∠ ECB are on same line

  • Now for triangle △BCE:

  • Now from figure angle ∠ CBE and ∠ y are on same line

Answer 10 (A)

  • For Triangle △MQN

  • From figure:
  • given

  • Now, from figure Angle ∠ MQN and ∠ y are on same line
  • Therefore

  • Now, Angle ∠ PQO and ∠ MQN are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

  • For Triangle △PQO

  • Now from figure, Angle ∠ OPQ and ∠ x are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

Answer 11 (A)

  • For Triangle △ABD
  • Now, we know that for △ABD

  • From figure line EF is perpendicular to line BD
  • Therefore
  • Now for triangle △EDF

  • Now from figure angle ∠ FED and ∠ y are on same line

Answer 12 (A)

  • Given that Angle ∠ CAB is twice the angle ∠ PBN than find the value of x.

  • From figure Angle ∠ PBN and ∠ CBA are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

  • Now for Triangle △CAB

  • From figure Angle ∠ BCA and ∠ x are vertically opposite angle and vertically opposite angle are always same.
  • Therefore

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