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Question Number 69098 by rajesh4661kumar@gmail.com last updated on 20/Sep/19

Commented by Kunal12588 last updated on 20/Sep/19

its really easy just construct a line through  F parallel to AB & CD. and remember the  property of alternate interior angles and  consectutive interior angles

$${its}\:{really}\:{easy}\:{just}\:{construct}\:{a}\:{line}\:{through} \\ $$$${F}\:{parallel}\:{to}\:{AB}\:\&\:{CD}.\:{and}\:{remember}\:{the} \\ $$$${property}\:{of}\:{alternate}\:{interior}\:{angles}\:{and} \\ $$$${consectutive}\:{interior}\:{angles} \\ $$

Commented by $@ty@m123 last updated on 20/Sep/19

Commented by Henri Boucatchou last updated on 20/Sep/19

Answered by $@ty@m123 last updated on 20/Sep/19

Draw a st. line through F  parallel to AB and CD.  Let q=x+y as shown in figure.  We have,  p+x=180^o  −−(1)  y=r −−−−(2)  Add (1) and (2)  p+x+y=180^o +r  ⇒ p+q−r=180^o

$${Draw}\:{a}\:{st}.\:{line}\:{through}\:{F} \\ $$$${parallel}\:{to}\:{AB}\:{and}\:{CD}. \\ $$$${Let}\:{q}={x}+{y}\:{as}\:{shown}\:{in}\:{figure}. \\ $$$${We}\:{have}, \\ $$$${p}+{x}=\mathrm{180}^{\mathrm{o}} \:−−\left(\mathrm{1}\right) \\ $$$${y}={r}\:−−−−\left(\mathrm{2}\right) \\ $$$${Add}\:\left(\mathrm{1}\right)\:{and}\:\left(\mathrm{2}\right) \\ $$$${p}+{x}+{y}=\mathrm{180}^{\mathrm{o}} +\mathrm{r} \\ $$$$\Rightarrow\:{p}+{q}−{r}=\mathrm{180}^{\mathrm{o}} \\ $$

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