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In the figure, arms $BA$ and $BC$ of $\angle ABC$ are respectively parallel to arms $ED$ and $EF$ of $\angle DEF$. Prove that $\angle ABC + \angle DEF = 180^o$."

Academic Mathematics NCERT Class 9

Given:

In the figure, arms $BA$ and $BC$ of $\angle ABC$ are respectively parallel to arms $ED$ and $EF$ of $\angle DEF$.

To do:

We have to prove that $\angle ABC + \angle DEF = 180^o$.

Solution:

Produce $BC$ to $H$ intersecting $ED$ at $G$.

$AB \parallel ED$

This implies,

$\angle ABC = \angle EGH$.......…(i) (Corresponding angles)

$BH \parallel EF$

This implies,

$\angle EGH + \angle DEF = 180^o$ (Sum of co-interior angles is $180^o$)

$\angle ABC + \angle DEF = 180^o$ [From (i)]

Hence proved.

Updated on: 10-Oct-2022

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