# 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 =

• 20°

• 40°

• 60°

• 80°

#### 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?

#### APPEARS IN

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