Question

Q14.In the adjacent figure, AB =AC and ∠C = 48o

. Find ∠A and ∠B.

Answer 1

Given, AB = AC

∠ABC=∠ACB=x (Isosceles triangle property)

In △ABC

∠ABC+∠ACB+∠ABC=180 (Sum of angles of triangle)

x+x+48=180

2x=132

x=66

∘

∠BCA=∠BCD+∠DCB=66

∠BCD=66−18

∠BCD=48

∘

Now, In △BCD

Sum of angles of triangle = 180

∠BCD+∠BDC+∠DBC=180

48+∠BDC+66=180

∠BDC=66

∘

Since, ∠BDC=∠DBC

hence, BD=CD (Isosceles triangle property)

Thus, △BDC is an isosceles triangle.