Question

1.5 triangles
score: 12.33/16 answered: 15/16
question 9

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°, 25°, 95° yes no explain:
b. angles 31°, 59°, 90° 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 \(30^{\circ},25^{\circ},95^{\circ}\), the sum is \(30 + 25+95=150^{\circ}\).

Step3: Calculate the sum for part b

For angles \(31^{\circ},59^{\circ},90^{\circ}\), the sum is \(31 + 59+90 = 180^{\circ}\).

Answer:

a. no, because \(30 + 25+95 = 150
eq180\)
b. yes, because \(31 + 59+90=180\)