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 measure (degrees) ∠a 40 ∠b ∠c

Explanation:

Step1: Consider the case when 40° is the non - congruent angle

Let the non - congruent angle be ∠A = 40°. In an isosceles triangle, the other two angles are equal. Let ∠B=∠C. Using the angle - sum property of a triangle (∠A + ∠B+∠C = 180°), we substitute ∠A = 40° and ∠B = ∠C. So, 40°+2∠B = 180°. Then 2∠B=180° - 40°=140°, and ∠B = ∠C = 70°.

Step2: Consider the case when 40° is one of the congruent angles

Let ∠A = ∠B = 40°. Then, using the angle - sum property of a triangle (∠A + ∠B+∠C = 180°), we substitute ∠A = 40° and ∠B = 40°. So, 40°+40°+∠C = 180°. Then ∠C=180°-(40° + 40°)=100°.

Answer:

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