Question

In the Given fig AB ll CD ; BC ll DE then find the value of x and y ..... Help dont give useless...answer or I may report and first and correct answer will get the brainarrest ​

Answer 1

Answer:

$\bigstar GIVEN:$

• AB║CD, BC║DE.
• ∠BCD=105°.
• ∠DCE=24°.

$\bigstar TO FIND:$

• x=?
• y=?

$\bigstar SOLUTION:$

Okay, lets rock this question!!!!

TO FIND X:

We know that AB║CD and BC actually forms a transversal.

So, ∠ABC=∠BCD  [Alternate interior angles are equal]

3x°=105°

x=105°÷3°

x=35°.

We found the value of x so easily!!!

TO FIND Y THERE ARE TWO METHODS:

METHOD -1

Look at point C.

We know that by linear pair:

∠BCA+∠BCD+∠DCE=180°

Substitute ∠BCD=105°, ∠DCE=24°

∠BCA+105°+24°=180°

∠BCA=180°-105°-24°

∠BCA=51°

Now, we know that DE║BC and AE actually forms a transversal.

∴∠BCA=y   [Corresponding angles]

∴y=51°.

METHOD -2

We know that BC║DE and CD forms a transversal.

∴∠BCD=∠CDE  [Alternate interior angles]

105°=∠CDE.

Now, look at ΔDCE. We can use angle sum property of triangles:

∠CDE+∠DEC+∠DCE=180°

Substitute ∠CDE=105°, ∠DCE=24°, ∠DEC=y.

105+24+y=180°

y=180°-105°-24°

y=51°

$\bigstar CONCLUSION:$

• x=35°
• y=51°.

${\huge{\mathfrak{\underbrace{\blue{HOPE \:\: THIS \:\: HELPS \:\: :D}}}$