Question

In given parallelogram ABCD , find the values of ∠ ABC , ∠ECF and ∠CDF if

∠ECB = 50° and ∠CFD and ∠CEB are right angles.
Guys it's very urgent pls give the answer​

Answer 1

Given: AB C D is a parallelogram, such that ∠AD E =50°, ∠ AC E= ∠ B ED=90°

To find: ∠ EA C + ∠ A BC - 2 ∠DA C

Solution: In parallelogram AB CD

∠ AC E= ∠ B ED=90°

∴ ∠ CA B = ∠ E BA = 90° [ opposite angles of a parallelogram are equal]

∵Parallelogram A B CD is a rectangle.

In Δ ACE and ΔBC E

AC =BE [opposite sides of rectangle]

∠ ACE = ∠B EC [each being 90°]

A E = B C [ Diagonals of a rectangle are equal]

Δ ACE ≅ ΔBC E [SSS]

∠ C A E = ∠ E B C [C P CT]

In ΔDA C

∠ D + ∠ DA C + ∠ AC D =180°[ angle sum property of triangle]

50° +∠ DA C + 90° =180°

∠ DA C =180° - 90°-50°

∠ DA C =40°

now, ∠ EA C + ∠ A BC - 2 ∠DA C

= ∠ E B C + ∠ A BC - 2 ∠DA C [ As,∠ C A E = ∠ E B C]

= ∠A BE - 2× 40°

= 90° - 80°

=10°

So,the value of ,∠ EA C + ∠ A BC - 2 ∠DA C=10°