Question

Find the interior angles of the following triangles:

Answer 1

In ABC,
AB = AC
⇒ ∠ACB = ∠ABC   ....(1)(angles opposite two equal sides are equal)
Now, ∠ACB + ∠ACD = 180°     ...(linear pair)
⇒ ∠ACB = 180° - ∠ACD
⇒ ∠ACB = 180° - 105°
⇒ ∠ABC = 75°
⇒ ∠ABC = 75°     ....[From (1)]
By angle sum property, in ΔABC
∠ABC + ∠ACB - ∠BAC = 180°
⇒ 75° + 75° + ∠BAC = 180°
⇒  150° + ∠BAC = 180°
⇒  ∠BAC = 180° - 150°
⇒ ∠BAC = 30°
Hence, in ΔABC, ∠A = 30°, ∠B = 75° and ∠C = 75°.