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If angle2 is-congruent-to angle6, which must be true about angle2? angle2 is-congruent-to angle5 angle2 is complementary to angle5. mangle2 = mangle8 angle2 is supplementary to angle8.

Sagot :

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).

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