Mathematics

In the adjoining figure, we find :

In the adjoining figure, we find : Inequalities, Concise Mathematics Solutions ICSE Class 9.
  1. AB = AC

  2. BC > AB

  3. AB > BC

  4. AC = BC

Triangles

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Answer

From figure,

DBC is a straight line.

∴ ∠ABD + ∠ABC = 180°

⇒ 125° + ∠ABC = 180°

⇒ ∠ABC = 180° - 125° = 55°.

We know that,

Exterior angle is equal to the sum of two opposite interior angle.

∴ Ext. ∠A = ∠ABC + ∠ACB

⇒ 115° = 55° + ∠ACB

⇒ ∠ACB = 115° - 55° = 60°.

In △ ABC,

By angle sum property of triangle,

⇒ ∠ABC + ∠ACB + ∠BAC = 180°

⇒ 55° + 60° + ∠BAC = 180°

⇒ 115° + ∠BAC = 180°

⇒ ∠BAC = 180° - 115° = 65°.

Since, ∠BAC > ∠ACB,

∴ BC > AB (If two angles of a triangle are unequal, the greater angle has the greater side opposite to it.)

Hence, Option 2 is the correct option.

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