In the given figure, the arms of two angles are parallel. If ∠ABC= 70^{o}, then find:

(i) ∠DGC

(ii) ∠DEF

(i) From the figure, it is clear that AB is parallel to DG and there is a transversal line BC that is intersecting them

Therefore,

∠DGC = ∠ABC (Corresponding angles)

As, it is given in the question that:

∠ABC = 70^{o}

Therefore,

∠ABC = ∠DGC = 70^{o}

Hence,

The value of ∠DGC is equal to 70^{o}

(ii) From the figure, it is clear that BC is parallel to EF and there is a transversal line DE that is intersecting them

Therefore,

∠DEF = ∠DGC (Corresponding angles)

As, from result of (i) it is clear that:

∠DGC = 70^{o}

Therefore,

∠DGC = ∠DEF = 70^{o}

Hence,

The value of ∠DEF is equal to 70^{o}

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