Question

in the given figure,ac and bd intersect at e such that be is equal = ec abe=70 and dce=80 if bac = 3/2 cde then bec​

Answer 1

Answer:

Given that,

⇒ ∠ABE = 70°

⇒ ∠DCE = 80°

⇒ BC = EC

Let us assume Angle CDE = x°.

According to the question,

⇒ ∠ BAC = 1.5 ( ∠ CDE )

⇒ ∠ BAC = 1.5 ( x° ) = 1.5x

Also, since AC and BD intersect at E, Angles AEB and DEC are equal as they are vertically opposite angles.

Now, Consider Δ ABE and Δ DCE:

According to angle sum property, sum of all interior angles of a triangle is equal to 180°. Using that we get:

In Δ ABE:

⇒ 1.5 x + 70° + ∠ AEB = 180°   ...(i)

In Δ DCE:

⇒ x + 80° + ∠ DEC = 180°   ...(ii)

Equating the LHS of (i) and (ii) we get:

⇒ 1.5 x + 70° + ∠ AEB = x + 80° + ∠ DEC

Since ∠ AEB and ∠ DEC  are equal we can cancel them. Hence we get:

⇒ 1.5x + 70° = x + 80°

⇒ 1.5x - x = 80° - 70°

⇒ 0.5x = 10°

⇒ x = 10/0.5 = 20°

Hence the value of x (∠CDE) is 20°.

Therefore in Δ DCE,

⇒ ∠ DEC = 180° - 80° - x°

⇒ ∠ DEC = 180° - 80° - 20°

⇒ ∠ DEC = 80°

Now consider the line BD. The angles DEC and BEC are lying along the straight line. Hence they are supplementary.

⇒ ∠ DEC + ∠ BEC = 180°

⇒ 80° + ∠ BEC = 180°

⇒ ∠ BEC = 180° - 80°

⇒ ∠ BEC = 100°

Hence Option (B) is the correct answer.

Answer 2

Answer:

Appropriate Question :-

• In the given figure,ac and bd intersect at e such that be is equal = ec abe=70 and dce=80 if bac = 3/2 cde then bec.

Answer :-

• Check the given attacchment above:

Therefore,

$\sf \pink{ \therefore \: Correct \: option \: is \: ( B )}$