Question

In figure if AE || DC and AB = AC, find the value of ∠ABD

Answer 1

Given :

AE || DC and AB = AC

To find :

 the value of ∠ABD

 

Solution :  

From figure we have, ∠EAF  = 70°

 

$\rm : \implies\: ∠EAF = ∠BCA \: [Corresponding angles]</p><p>$

$\rm : \implies\: ∠BCA = 70° ……………(1)$

$\rm \bf \: We \: have, AB = AC, then$

$\rm : \implies\: ∠CBA = ∠BCA [Angles \: opposite \: to \: equal \: sides \: are \: equal]$

$\rm : \implies \: ∠CBA = 70°$

$\rm \: [From \: eq \: 1]</p><p>$

Now,

$\rm : \implies ∠ABD + ∠CBA = 180° [Linear \: pair] \:$

$\rm : \implies ∠ABD + 70° = 180°$

$\rm : \implies∠ABD = 180° - 70°$

$\rm : \implies∠ABD = 110 \degree$

Hence , the value of ∠ABD is 110°.

Answer 2

ANSWER

_____________

It is given that

<MAE = 70°

ZNAC 70°(Vertically apposite

angle)

Now ZMAE + ZEAB + <BAC =180°

(linear pair)....

(1)

Similarly LEAB +<BAC +ZNAC = 180° (linear pair) . (2)

From equation (1) we have

ZEAB + <BAC = 180°

= 110°

Now <FCA = <DBA (same exterior angle)

ZACF = LEAC (Interior angle)

Now

ZEAC = 110°

So ZAFC 110°

Since ZAFC =<ABD

Hence (b)ZABD = 110°.

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