Question

In the figure AC Is the bisector of both
.
<A and <C also <B = 90°
a)<b
b) If AB = 4cm
CD = 3cm
Find Apand AC
A
B
'D
3
С​

Answer 1

Answer:

In △ABC,

⇒  AB=AC                [ Given ]

⇒  ∠ABC=∠ACB           [ Base angles of equal sides are also equal. ]

⇒  ∠ABC=75o

∴  ∠ACB=75o

⇒  ∠ABC+∠ACB+∠BAC=180o

⇒  75o+75o+x=180o

⇒  150o+x=180o

⇒  x=30o.

It is given that, AC bisects ∠A

∴  ∠BAC=∠CAD

∴ ∠CAD=30o

In △ACD,

⇒  AD=CD                [ Given ]

⇒  ∠CAD=∠ACD      [ Base angles of equal sides are also equal. ]

∴  ∠ACD=30o

⇒  ∠CAD+∠ACD+∠CDA=180o

⇒  30o+30o+y=180o

⇒  60o+y=180o

⇒