Question

in fig. 16.22, BE is parallel to CD, BA = BC, <ABE = 20° and <DCG = 60°. Determine <FAC. ​

Answer 1

Answer:

<DCG =<EBC (corresponding angles of parallel lines)

< EBC = 60 ° [ <DCG =60°]

Now,

< ABC = < EBC - <EBA

or, <ABC = 60 - 20 = 40

Now, BA = BC [ given]

Therefore, <BAC = <ACB

Now,

<ABC + <BAC + <ACB = 180

or, 40 + 2<BAC = 180

or, 2<BAC = 180 - 40 = 140

or, <BAC = 70

Finally,

<FAC = <FAB - <BAC

or, <FAC = 180 - 70 [ FB is a straight line]

or, <FAC = 110