In the given figure, BD || CE; AC = BC, ∠ABD = 20° and ∠ECF = 70°. Find ∠GAC.

From figure,

BF is the transversal on parallel lines BD and CE.

⇒ ∠DBC = ∠ECF = 70° (Corresponding angles are equal)

⇒ ∠DBC = 70°

⇒ ∠DBA + ∠ABC = 70°

⇒ 20° + ∠ABC = 70°

⇒ ∠ABC = 70° - 20°

⇒ ∠ABC = 50°.

In △ABC,

AC = BC

⇒ ∠ABC = ∠BAC = 50° (Angles opposite to equal sides in a triangle are equal)

⇒ ∠BAC + ∠GAC = 180° (Linear pair)

⇒ 50° + ∠GAC = 180°

⇒ ∠GAC = 180° - 50°

⇒ ∠GAC = 130°.

Hence, ∠GAC = 130°.