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) 42°, 58°, 34°\t\t
(b) 70°, 45°, 65°\t\t
(c) 14°, 43°, 33°\t\t
(d) 42°, 18°, 120°\t\t

Explanation:

To determine if three angle measures can form a triangle, we use the property 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) - \(42^\circ\), \(58^\circ\), \(34^\circ\)

Calculate the sum of the angles:
\[
42 + 58 + 34 = 134
\]
Since \(134^\circ
eq180^\circ\), these angles cannot be the angle measures of a triangle.

Step 2: Analyze set (b) - \(70^\circ\), \(45^\circ\), \(65^\circ\)

Calculate the sum of the angles:
\[
70 + 45 + 65 = 180
\]
Since \(180^\circ = 180^\circ\), these angles can be the angle measures of a triangle.

Step 3: Analyze set (c) - \(14^\circ\), \(43^\circ\), \(33^\circ\)

Calculate the sum of the angles:
\[
14 + 43 + 33 = 90
\]
Since \(90^\circ
eq180^\circ\), these angles cannot be the angle measures of a triangle.

Step 4: Analyze set (d) - \(42^\circ\), \(18^\circ\), \(120^\circ\)

Calculate the sum of the angles:
\[
42 + 18 + 120 = 180
\]
Since \(180^\circ = 180^\circ\), these angles can be the angle measures of a triangle.

Answer:

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

So we mark:
(a) → Cannot be angle measures of a triangle
(b) → Can be angle measures of a triangle
(c) → Cannot be angle measures of a triangle
(d) → Can be angle measures of a triangle