In △ABC, <C = 54º, the perpendicular bisector of AB at D meets BC at E. If <EAC = 42°; then what is the value (in degrees) of <ABC?

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In △ABC,

A25

B42

C45

D50

Answer:

<C = 54° and <EAC = 42°, So <AEC = 84°

(sum of all angles of triangle = 180º)

:. <BEA = 180 - 84 = 96°

: DE bisects AB perpendicularly, so angle made by BD and DA should be equal.

:: <DBE + <BED + <EDB = 180°

:: <DBE + 96/2 + 90 = 180

:. <ABC = <DBE = 180 - 90 - 48 = 42°

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