In the given figure, AB || CD || EF. If ∠ABC = 85°, ∠BCE = x° and ∠CEF = 130°, then x = ?

Question

In the given figure, AB || CD || EF. If ∠ ABC = 85°, ∠ BCE = x° and ∠ CEF = 130°, then x = ?

Philoid · Accepted Answer

According to question,

AB || EF

EF || CD (AB is produced to F, CF is traversal)

FEC=130^o

Now, BFC + BFO = 180^o(Sum of angles of Linear pair is 180^o)

BFO = 180^o – 130^o = 50^o

Now in triangle BOF, we have

ABO = BFO + BOF

85 = 50 + BOF

BOF = 85 – 50 =35^o

So, x = ^o