Question

in the
adjoining figure ,Ab= Ac,
and angle ACD = 18°
angle ACD = 18° show
that bc=Cd

​

Answer 1

Answer:

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