# 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

(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.

(a)

## (3) Find the Following Angles

(a)

Find following angles

## (4) Find the Following Angles

(a)

Find following angles

(a) EC

(a)

(a)

(a)

## (12) Find the Value of X

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

• 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;

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:

• 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:

• 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;

• 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

• 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

• 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

• 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

• 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

• 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.
• 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

• 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

• 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

• 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

• 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