Question

A, B & C lie on a straight line. G, B & F lie on a different straight line. D, E & F lie on a straight line parallel to AC. DEB = 104°. GBA = 24°. Work out EBF.

Answer 1

The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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