Question

triangle abc is an isosceles triangle and the measure of one of the angles is 40°. list a set of possible angle measures in this triangle.
angle\tmeasure (degrees)
∠a\t40
∠b
∠c

Explanation:

Step1: Case 1 - 40° is a base - angle

If ∠A = 40° is a base - angle, then since the triangle is isosceles, another base - angle can be equal. Let ∠B=40°. Using the angle - sum property of a triangle (the sum of the interior angles of a triangle is 180°), we find ∠C as follows:
∠C = 180°−40°−40° = 100°.

Step2: Case 2 - 40° is the vertex - angle

If ∠A = 40° is the vertex - angle, then the two base - angles (∠B and ∠C) are equal. Let ∠B = ∠C=x. Then, by the angle - sum property of a triangle, 40°+x + x=180°. Combining like terms gives 40° + 2x=180°. Subtracting 40° from both sides: 2x=180° - 40°=140°. Dividing both sides by 2, we get x = 70°. So ∠B = 70° and ∠C = 70°.

Answer:

Case 1: ∠A = 40°, ∠B = 40°, ∠C = 100°; Case 2: ∠A = 40°, ∠B = 70°, ∠C = 70°