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Standard IX

Mathematics

Exterior Angle of a Triangle = Sum of Opposite Internal Angles

The side B C ...

Question

The side BC of ∆ABC has been increased on both sides as shown. If ∠ABD = 105° and ∠ACE = 110°, find ∠A.

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Solution

We have:
$∠ A C D + ∠ A C E = 180 ° [Linear pair] \Rightarrow ∠ A C D + 110 ° = 180 ° \Rightarrow ∠ A C D = 70 °$
Side BC of triangle ABC is produced to D.
$∴ ∠ A B D = ∠ B A C + ∠ A C D [E xterior angle property] \Rightarrow 105 ° = ∠ B A C + 70 ° \Rightarrow ∠ B A C = 35 ° \Rightarrow ∠ A = 35 °$

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Q. Side BC of ∆ABC has been produced to D on left hand side and to E on right hand side such that ∠ABD = 125° and ∠ACE = 130°. Then ∠A = ?
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Side $B C$ of $Δ A B C$ has been produced to $D$ on left and to $E$ on right hand side of BC such that $∠ A B D = 125^{\circ}$ and $∠ A C E = 130^{\circ}$ . Then $∠ A =$ ?
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The side BC of ∆ABC has been increased on both sides as shown. If ∠ABD = 105° and ∠ACE = 110°, find ∠A.

We have: ∠ACD+∠ACE=180° Linear pair⇒∠ACD+110°=180°⇒∠ACD=70° Side BC of triangle ABC is produced to D. ∴∠ABD=∠BAC+∠ACD [Exterior angleproperty]⇒105°=∠BAC+70°⇒∠BAC=35°⇒∠A=35°