Question

which sets of measurements could be the interior angles of a triangle? select each correct answer. 10°, 90°, 100° 30°, 30°, 115° 15°, 15°, 150° 10°, 80°, 90° 60°, 60°

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is $180^{\circ}$.

Step2: Check option A

$10^{\circ}+90^{\circ}+100^{\circ}=200^{\circ}
eq180^{\circ}$, so it's not a triangle.

Step3: Check option B

$30^{\circ}+30^{\circ}+115^{\circ}=175^{\circ}
eq180^{\circ}$, so it's not a triangle.

Step4: Check option C

$15^{\circ}+15^{\circ}+150^{\circ}=180^{\circ}$, so it can be a triangle.

Step5: Check option D

$10^{\circ}+80^{\circ}+90^{\circ}=180^{\circ}$, so it can be a triangle.

Step6: Check option E

$60^{\circ}+60^{\circ}+60^{\circ}=180^{\circ}$, so it can be a triangle.

Answer:

C. $15^{\circ}, 15^{\circ}, 150^{\circ}$, D. $10^{\circ}, 80^{\circ}, 90^{\circ}$, E. $60^{\circ}, 60^{\circ}, 60^{\circ}$