Question

In Fig. 72, if AB || CD and AE || BD, then the value of x is


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Answer 1

Answer:

If AB || CD

then

angle B+angle D=180°(co interior angles)

angle B+84=180

angle B=96°

also

if AE || BD

then

angle B+angle A=180°(co interior angles)

angle A+96=180

angle A=84°

but we need x

From the figure, it's a Pentagon

and sum of all interior angles of a Pentagon=540°

that is

angle A+angle B+angle C+angle D+angle E=540°

84+96+132+84+3x=540

396+3x=540

3x=144

x=144÷3

x=48°

Therefore the value of x=48°

angle E=3x=3×48=114°

hope it helps