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: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.

Step2: Case 1: ∠A = 40° is one of the equal angles

If ∠A=∠B = 40°, then ∠C=180°-(40° + 40°)=100°.

Step3: Case 2: ∠A = 40° is not one of the equal angles

Let ∠B = ∠C. Then 40°+2∠B = 180°. Solving for ∠B, we get 2∠B=180° - 40°=140°, so ∠B = ∠C = 70°.

Answer:

Angle	Measure (degrees)
∠B	40
∠C	100

or

Angle	Measure (degrees)
∠B	70
∠C	70