Question

Lines and Angles
pg 225.
10.In the given figure, AB || CD. Find the value of x.
D
B
130°
C
to
А
20°
E​

Answer 1

Answer:X= 110°

Step-by-step explanation:

Expand CD toward AE intersecting at F such that CF║AB.

∵ DCF is a straight line

so,  ∠ DCE + ∠ FCE = 180°

130° + ∠ FCE = 180° ( given  ∠DCE = 130°)

So  ∠FCE = 180°-130° = 50°

Now angle FCE = 50 degree.

Consider triangle FCE  

∠s (FCE + CEF + CFE) = 180°

50°+ 20° + ∠CFE = 180°  (∵ ∠CEF = 20° given)

By solving this equation, we get

angle CFE = 110  degree.

Now we have CF parallel to AB

So angle CFE = BAF { Corresponding angle }

Hence, angle CFE = BAF = 110°

i.e., ∠BAF = x = 110°