Question

In figure AB ll ED what is the value of x?

Answer 1

Answer:

In given figure AB∥ED and EF∥CD

∠DEF=90−∠GEF=90−20=70

0

Given that EF∥CD and line ED join these

∴∠DEF=∠EDC=70

0

Join BD

∠CBD=90−∠ABC=90−50=40

0

∠CDB=90−∠CDE=90−70=20

0

In ΔBCD,

∠CBD+∠CDB+∠BCD=180

40+20+x=180

⇒x=180−40−20=120

0

Answer 2

$\huge \bold{answer : }$

Extend line AB,BC,DE by dashed line for better understanding of parallel lines and transversal

< EDC+ <DCB = 180°

(consecutive interior angles of transversal on parallel lines are supplementary)

<DCB = 180°- < EDC

<DCB =180°-75°

<DCB = 105°

Since AB is parallel to DC

So, <DCB and x forms pair of alternate interior angles,and we know that

they are equal

<DCB = x° (pair of alternate interior angle)

x° = 105°

Hope it helps you.

Note: angle DCB is written as <DCB