The degree measures of the two outer angles of the triangle at different vertices are equal.

The degree measures of the two outer angles of the triangle at different vertices are equal. the perimeter of the triangle is 68 cm, and one of the sides is 12 cm. Find the lengths of the other two sides.

The outside angle at the apex of the triangle is 180 – the inside angle. Or it is equal to the sum of 2 other angles of the triangle not adjacent to it. Thus β + γ = α + β (since the 2 outer corners are equal). Hence γ = α -> isosceles triangle. The condition does not indicate which side is 12, therefore, 2 answers are possible in this problem. If 12 is equal to the AC side, then AB and BC = (68 – 12) / 2 = 28 If 12 is equal to the AB (BC) side, then one of the sides = 12, and the other 68 – 12 – 12 = 44.