Mathematics
Side BA is produced upto point D and side BC upto point E such that ∠DAC = 110° and ∠ACE = 125°. Then the largest side of the triangle ABC is
AB
BC
AC
none of these
Triangles
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Answer
From figure, ∠DAC and ∠BAC forms linear pair.
⇒ ∠DAC + ∠BAC = 180°
⇒ 110° + ∠BAC = 180°
⇒ ∠BAC = 180° - 110°
⇒ ∠BAC = 70°
Similarly, ∠ACE and ∠ACB forms linear pair.
⇒ ∠ACE + ∠ACB = 180°
⇒ 125° + ∠ACB = 180°
⇒ ∠ACB = 180° - 125°
⇒ ∠ACB = 55°
In ΔABC, according to angle sum property,
⇒ ∠ABC + ∠ACB + ∠BAC = 180°
⇒ ∠ABC + 55° + 70° = 180°
⇒ ∠ABC + 125° = 180°
⇒ ∠ABC = 180° - 125°
⇒ ∠ABC = 55°
As we know that the side opposite to the largest angle in a triangle is the longest side.
Since, ∠BAC is the largest angle of the triangle.
So, BC is the largest side of the triangle ABC.
Hence, option 2 is the correct option.
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Statement (1): In the given figure, AC = DC = BD and ∠B = 30°.
Statement (2): ΔCAD is equilateral.
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Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.