Question

In the given fig. DE || BC, LADE =70° and LBAC=50°, then angle
LBCA =
A
E
B
OR
I
In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE
parallel to BC?
А.
E
B​

Answer 1

Question 1) :- In the given fig. DE || BC, ∠ADE =70° and ∠BAC=50°, then ∠BCA = ?

Solution :-

given that,

→ ∠ADE =70°

→ ∠BAC=50°

So,

→ ∠ABC = 70° (since DE || BC, corresponding angles.)

Now, in ∆ABC,

→ ∠BAC + ∠ABC + ∠BCA = 180° (angle sum property.)

→ 50° + 70° + ∠BCA = 180°

→ 120° + ∠BCA = 180°

→ ∠BCA = 180° - 120°

→ ∠BCA = 60° (Ans.)

______________

Question 2) :- In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC ?

Solution :-

we know that, if DE is parallel to BC :-

• AD / AB = AE / AC .

checking by putting given values we get,

→ AD/(AD + DB) = AE / AC

→ 2/(2 + 3) = 3.5 / 7

→ 2/5 ≠ 1/2 .

Therefore, we conclude that, DE is not parallel to BC.

Learn more :-

ABCD is a rhombus with A = 60° , BC = (3x+5)cm , CD =(6x-10)cm and AC =(3y-1)cm. Find

x and y.

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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