The document RD Sharma Solutions (Part - 3) - Ex-14.2, Lines and Angles, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**In Fig., AB || CD and AC || BD. Find the values of x, y, z.**

(i) Since AC || BD and CD || AB,* *ABCD is a parallelogram.

âˆ CAB + âˆ ACD = 180Â° (Sum of adjacent angles of a parallelogram)

âˆ´ âˆ ACD = 180Â° âˆ’ 65Â° = 115Â°

âˆ CAD = âˆ CDB = 65Â° (Opposite angles of a parallelogram)

âˆ ACD = âˆ DBA = 115Â° (Opposite angles of a parallelogram)

(ii) Here,

AC || BD and CD || AB

âˆ DAC = *x* = 40Â° (Alternate interior angle)

âˆ DAB = *y* = 35Â° (Alternate interior angle)

**In Fig., state which lines are parallel and why?**

Since âˆ ACD and âˆ CDE are alternate and equal angles, so

âˆ ACD = 100Â° = âˆ CDE

âˆ´ AC || EF

In Fig. 87, the corresponding arms of âˆ ABC and âˆ DEF are parallel. If âˆ ABC = 75Â°, find âˆ DEF.

**Construction :** Let G be the point of intersection of lines BC and DE.

âˆµ AB || DE and BC || EF

âˆ´ âˆ ABC=âˆ DGC=âˆ DEF=75Â°âˆ ABC=âˆ DGC=âˆ DEF=75Â° (Corresponding angles)