Question

which set of angle measures can be used to construct an acute scalene triangle? 60°, 60°, 60° 40°, 50°, 90° 40°, 50°, 60° 40°, 60°, 80°

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is $180^{\circ}$. Also, an acute - angled triangle has all angles less than $90^{\circ}$, and a scalene triangle has all angles of different measures.

Step2: Check the first option

For the angles $60^{\circ},60^{\circ},60^{\circ}$, the sum is $60 + 60+60=180^{\circ}$, but all angles are equal, so it is an equilateral triangle, not scalene.

Step3: Check the second option

For the angles $40^{\circ},50^{\circ},90^{\circ}$, since one angle is $90^{\circ}$, it is a right - angled triangle, not an acute - angled triangle.

Step4: Check the third option

For the angles $40^{\circ},50^{\circ},60^{\circ}$, the sum is $40 + 50+60 = 150^{\circ}
eq180^{\circ}$, so it cannot form a triangle.

Step5: Check the fourth option

For the angles $40^{\circ},60^{\circ},80^{\circ}$, the sum is $40+60 + 80=180^{\circ}$, all angles are less than $90^{\circ}$ (acute), and all angles have different measures (scalene).

Answer:

$40^{\circ},60^{\circ},80^{\circ}$