Question

In the figure , what value of x will make EF parallel CD if AB parallel CD .
angle ABC = 65 degrees
angle BCE = 25 degrees
angle CEF = x​

Answer 1

Given:

AB is parallel to CD

$\bold{\angle ABC = 65^{o}}$

$\bold{\angle BCE = 25^{o}}$

$\bold{\angle CEF = x}$

To Find:

Value of x if EF and CD parallel.

Step-by-step explanation:

Before start let us extend the line CE to G point as shown in the attached figure

From the givens we know that AB is parallel to CD

∴ From roles of geometry we can say,

$\bold {\angle ABC = \angle BCD}$

$=>\bold {\angle ABC = \angle BCE+ \angle ECD }$

$\bold{=> 65^o=25^o+\angle ECD}$

$\bold{=> \angle ECD = 40^o}$

Now, EF is parallel to CD then

$\bold {\angle ECD = \angle GEF}$

∴$\bold{\angle GEF = 40^o}$

Now, from the attached figure

$\bold{\angle GEF + \angle CEF = 180^o}$   (∵ CEG is a straight line)

$\bold{=>\angle GEF + x= 180^o}$

$\bold{=>40^o+ x= 180^o}$

$\bold{=>x= 140^o}$

∴Value of x will be $\bold{140^o}$ which make EF and CD parallel.

Answer 2

Answer:

Given:

AB is parallel to CD

\bold{\angle ABC = 65^{o}}∠ABC=65o

\bold{\angle BCE = 25^{o}}∠BCE=25o

\bold{\angle CEF = x}∠CEF=x

To Find:

Value of x if EF and CD parallel.

Step-by-step explanation:

Before start let us extend the line CE to G point as shown in the attached figure

From the givens we know that AB is parallel to CD

∴ From roles of geometry we can say,

\bold {\angle ABC = \angle BCD}∠ABC=∠BCD

= > \bold {\angle ABC = \angle BCE+ \angle ECD }=>∠ABC=∠BCE+∠ECD

\bold{= > 65^o=25^o+\angle ECD}=>65o=25o+∠ECD

\bold{= > \angle ECD = 40^o}=>∠ECD=40o

Now, EF is parallel to CD then

\bold {\angle ECD = \angle GEF}∠ECD=∠GEF

∴\bold{\angle GEF = 40^o}∠GEF=40o

Now, from the attached figure

\bold{\angle GEF + \angle CEF = 180^o}∠GEF+∠CEF=180o   (∵ CEG is a straight line)

\bold{= > \angle GEF + x= 180^o}=>∠GEF+x=180o

\bold{= > 40^o+ x= 180^o}=>40o+x=180o

\bold{= > x= 140^o}=>x=140o

∴Value of x will be \bold{140^o}140o which make EF and CD parallel.