Question

1.5 triangles
score: 6.33/16 answered: 7/16
question 8

1. know the angle measure requirements of a triangle (triangle angle sum theorem).

determine if the given angles will make a triangle. explain why or why not.
a. angles 30°, 40°, 20°
yes no explain:
b. angles 35°, 90°, 55°
yes no explain:

Explanation:

Step1: Recall the Triangle Angle Sum Theorem

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Calculate the sum for part a

For angles \(30^{\circ},40^{\circ},20^{\circ}\), the sum is \(30 + 40+20=90^{\circ}\).
Since \(90^{\circ}
eq180^{\circ}\), these angles do not form a triangle.

Step3: Calculate the sum for part b

For angles \(35^{\circ},90^{\circ},55^{\circ}\), the sum is \(35 + 90+55 = 180^{\circ}\).
Since \(180^{\circ}=180^{\circ}\), these angles form a triangle.

Answer:

a. no. Explanation: The sum of the angles \(30 + 40+20 = 90^{\circ}
eq180^{\circ}\).
b. yes. Explanation: The sum of the angles \(35 + 90+55=180^{\circ}\).