Question

Find the interior angles of the following triangles:

Answer 1

In ΔABD,
AD = BD                     ....(given)
⇒ ∠ABD = ∠BAD      ....(angles opposite to two equal sides are equal)
Now, ∠ABD = 37°     ....(given)
⇒ ∠BAD = 37°
By exterior angle property,
∠ADC =∠ABD  + ∠BAD
⇒ ∠ADC = 37° + 37° = 74°
In ΔADC,
AC = DC                     ....(given)
⇒ ∠ADC = ∠DAC      ....(angles opposite to two equal sides are equal)
⇒ ∠DAC = 74°
Now, ∠BAC = ∠BAD + ∠DAC
⇒ ∠BAC = 37° + 74° = 111°
In ΔABC,
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 111° + 37° + ∠ACB = 180°
⇒ ∠ACB = 180° - 111° - 37° = 32°
Hence, the interior angles of ΔABC are 37°, 111° and 32°.