Question

for each set of three measures, determine if they can be angle measures of a triangle.
angles\tcan be angle measures of a triangle\tcannot be angle measures of a triangle
(a) 31°, 132°, 141°\t○\t○
(b) 35°, 62°, 102°\t○\t○
(c) 150°, 15°, 15°\t○\t○
(d) 50°, 90°, 30°\t○\t○

Explanation:

To determine if three angle measures can form a triangle, we use the fact that the sum of the interior angles of a triangle is always \(180^\circ\). For each set of angles, we calculate their sum and check if it equals \(180^\circ\).

Step 1: Analyze set (a)

The angles are \(31^\circ\), \(132^\circ\), and \(141^\circ\).
Sum = \(31 + 132 + 141 = 304^\circ\)
Since \(304^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Step 2: Analyze set (b)

The angles are \(35^\circ\), \(62^\circ\), and \(102^\circ\).
Sum = \(35 + 62 + 102 = 199^\circ\)
Since \(199^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Step 3: Analyze set (c)

The angles are \(150^\circ\), \(15^\circ\), and \(15^\circ\).
Sum = \(150 + 15 + 15 = 180^\circ\)
Since the sum is \(180^\circ\), these can be angle measures of a triangle.

Step 4: Analyze set (d)

The angles are \(50^\circ\), \(90^\circ\), and \(30^\circ\).
Sum = \(50 + 90 + 30 = 170^\circ\)
Since \(170^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Answer:

• (a): Cannot be angle measures of a triangle
• (b): Cannot be angle measures of a triangle
• (c): Can be angle measures of a triangle
• (d): Cannot be angle measures of a triangle