Question

in the given figure AB parallel to CD, AFis parallel to ED , angle AF C is equal to 68DEGREE and Angle FED is equal to 42 degree find angle EFD

Answer 1

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Answer 2

Answer:

70°

Step-by-step explanation:

Given information: AB║CD, AF║ED, ∠AFC=68° and ∠FED=42°.

If a transversal line intersect two parallel lines, then corresponding angles are congruent.

AF║ED and CD is transversal line. So, angle AFC and angle EDF are corresponding angles.

$\angle AFC\cong \angle EDF$           (corresponding angles)

$68^{\circ}=\angle EDF$                       (∠AFC=68°)

Accoding to angle sum property, the sum of interior angles of a triangle is 180°.

In triangle DEF,

$\angle FE D+\angle EDF+\angle EFD=180^{\circ}$

$42^{\circ}+68^{\circ}+\angle EFD=180^{\circ}$

$110^{\circ}+\angle EFD=180^{\circ}$

$\angle EFD=180^{\circ}-110^{\circ}$

$\angle EFD=70^{\circ}$

Therefore the measure of angle EFD is 70°.