Question

The exterior angles obtained on producing the base of a triangle both ways are 104 degree and 136 degree find all the angles of the triangle

Answer 1

From the adjacent figure, 
the exterior angle ∠ACD=136°
∴, ∠ACB=180°-136°=44°
the other exterior angle, ∠ABE=104°
∴, ∠ABC=180°-104°=76°
∴, ∠BAC=180°-(∠ABC+∠ACB)
              =180°-(76°+44°)
              =180°-120°
              =60°
∴, the angles of the given triangle are: 76°,60° and 44° Ans.

Answer 2

In triangle ABC, Let the base angles be angle B and angle C.
angle B = 180-104 = 76 degrees
angle C = 180-136 = 44 degrees
Therefore, 
The third angle, that is, angle A = 180 - (76+44) = 180 - 120 = 60 degrees.
Hence,
          The angles of the triangle are 60 degree, 76 degree and 44 degree