Question

Show That AB || EF Show that's AB is parallel to EF

Answer 1

Answer:

Step-by-step explanation:

given- angle B = 60

           angle BCE = 36

            angle ECD = 30

          angle CEF = 150

To prove - AB||EF

Answer 2

GIVEN:-

• $\rm{\angle{FEC=150^{\circ}}\angle{ECD=30^{\circ}}}$

• $\rm{\angle{ABC=60^{\circ}}\angle{BCE=36^{\circ}}}$

TO SHOW

AB||CE

CONCEPT USED

• if the alternate angle are of two different angles are equal then lines are parallel

• if the alternate angle are of two different angles are equal then lines are parallel if Sum of two consecutive interior angle is 180° then lines are parallel.

Now,

$\implies\rm{\angle{ABC}=\angle{BCE}+\angle{ECD}}${Alternate angles}

$\implies\rm{66^{\circ}=36^{\circ}+30^{\circ}}$

$\implies\rm{66=66}$.

Hence, Alternate angles are equal so,

AB||CD...........1

Again,

$\implies\rm{\angle{CFE}+\angle{ECD}=180^{\circ}}$(Co-interior angle).

$\implies\rm{150^{\circ}+30^{\circ}=180^{\circ}}$

$\implies\rm{180^{\circ}=180^{\circ}}$.

Hence, EF||CD.....2.

From 1 and 2 we get AB||EF.

Hence, Proved.

MORE TO KNOW

• The corresponding angles are equal.

• The Vertically opposite angles are equal

• The pair of interior angles on the same side of transversal is Supplementary.