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In the Below Fig, Arms Ba and Bc of ∠Abc Are Respectively Parallel to Arms Ed and Ef of ∠Def. Prove that ∠Abc + ∠Def = 180°. - Mathematics

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In the below fig, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of
∠DEF. Prove that ∠ABC + ∠DEF = 180°.

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Solution

Given AB || DE, BC || EF

To prove: `∠`ABC + `∠`DEF =180°

Construction: produce BC to intersect DE at M

Proof: Since AB || EM and BL is the transversal

`∠`ABC = `∠`EML          [Corresponding angle]            ……(1)

Also,  

EF || ML and EM is the transversal

By the property of co-interior angles are supplementary

`∠`DEF + `∠`EML = 180°

From (i) and (ii) we have

∴`∠`DEF + `∠`ABC = 180°

Concept: Pairs of Angles
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.4 | Q 27 | Page 49

Video TutorialsVIEW ALL [1]

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