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The correct statement is that if ∠2 is congruent to ∠6, then ∠2 is supplementary to ∠8 i.e.option(D).
Given that the ∠2 is congruent to ∠6
∠5 + ∠6 =180° { a straight line is intersected by a line. as it is a straight line total angle=180°}
As the ∠2 is congruent to ∠6⇒ ∠5 + ∠2 =180°
⇒ ∠2 is supplementary to ∠5. i.e. option (B) is incorrect
as it is given as ∠2 is complementary to ∠5
⇒∠5 + ∠2 =180°{ as ∠2 is congruent to ∠6}
⇒ ∠2 =180°-∠5 i.e. option (A) is incorrect
⇒∠6 + ∠8 =180° { a straight line is intersected by a line. as it is a straight line total angle=180°}
⇒As, the ∠2 is congruent to ∠6⇒ ∠2 + ∠8 =180°
⇒∠8 =180° - ∠2 i.e. option(C) is incorrect
∠2 is supplementary to ∠8 i.e.option(D) is correct
Therefore, The correct statement is that if ∠2 is congruent to ∠6, then ∠2 is supplementary to ∠8 i.e.option(D).
complete question:image attached
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