Find the angles of an isosceles triangle if one of them is: 1) 45 °, 2) 94 °. How many solutions does the problem have?

1) One of the angles of the triangle is 45 °. There are two options: either this is the angle at the apex of the triangle (1) or this is the angle at the base of the triangle (b).

a) The angles at the base in an isosceles triangle are equal, we calculate their value:

(180 ° – 45 °): 2 = 135 °: 2 = 67.5 °.

Answer: the angles of the triangle are 45 °, 67.5 °, 67.5 °.

b) If 45 ° is the angle at the base, then the angle at the apex of the triangle is:

180 ° – (45 ° * 2) = 180 ° – 90 ° = 90 °.

Answer: The angles of the triangle are 45 °, 45 °, 90 °.

2) One of the angles of the triangle is 94 °. It cannot be an angle at the base, since there cannot be two obtuse angles in a triangle. Hence, this is the angle at the apex of the triangle. Let’s calculate the value of the angles at the base:

(180 ° – 94 °): 2 = 86 °: 2 = 43 °.

Answer: The angles of the triangle are 94 °, 43 °, 43 °.