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Question

In the following figure, l1,l2,l3 are parallel to each other. Find the value of BDC if BFE=BCD=50.

A
90°
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B
50°
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C
80°
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D
40°
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Solution

The correct option is C 80°

Given l1,l2,l3 are parallel to each other and BFE=BCD=50°.

From the figure,
CAB=90°
Then, CAB=FEB=90° (Corresponding angles)

Taking the BEF by angle sum property,
BEF+BFE+EBF=180°
90°+50°+EBF=180°
140°+EBF=180°
EBF=180°140°=40°

In triangle ABC, by angle sum property, we have
ABC+BCA+CAB=18040+BCA+90=180BCA=180130=50

Now, ACD+BDC=180° ( Co-interior angles)
ACD=BCA+BCD=50+50=100

100°+BDC=180°
BDC=180°100°=80°

Hence, BDC=80°.

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