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In a δAbc, If Ab = Ac and Bc is Produced to D Such that ∠Acd = 100°, Then ∠A = - Mathematics

MCQ

In a ΔABC, if AB = AC and BC is produced to D such that ∠ACD = 100°, then ∠A =

Options

  • 20°

  • 40°

  • 60°

  • 80°

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Solution

In the triangle ABC it is given that 

 AB = AC

 ∠ACD = 100°

We have to find ∠A

Now  ∠ACD +  ∠ACB = 180° (linear pair)

SinceAB = AC

So, ∠B =  ∠C (by isosceles triangle)

This implies that

 ∠B =∠C

= 180° - 100

= 80

Now, 

 ∠A + ∠B + ∠C = 180° (Property of triangle) 

∠A + 80° + 80° = 180°

                    ∠A = 180° - 160°

                    ∠A  = 20°

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 12 Congruent Triangles
Q 8 | Page 85
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