Question

for each set of three measures, determine if they can be angle measures of a triangle.

angles	can be angle measures of a triangle	cannot be angle measures of a triangle
(b) 53°, 125°, 23°	○	○
(c) 15°, 15°, 150°	○	○
(d) 90°, 40°, 30°	○	○

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 must be \(180^\circ\). For each set of angles, we calculate their sum and check if it equals \(180^\circ\).

Step 1: Analyze set (a) \(132^\circ, 31^\circ, 141^\circ\)

Calculate the sum: \(132 + 31 + 141 = 304^\circ\). Since \(304^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Step 2: Analyze set (b) \(53^\circ, 125^\circ, 23^\circ\)

Calculate the sum: \(53 + 125 + 23 = 201^\circ\). Since \(201^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Step 3: Analyze set (c) \(15^\circ, 15^\circ, 150^\circ\)

Calculate the sum: \(15 + 15 + 150 = 180^\circ\). Since the sum is \(180^\circ\), these can be angle measures of a triangle.

Step 4: Analyze set (d) \(90^\circ, 40^\circ, 30^\circ\)

Calculate the sum: \(90 + 40 + 30 = 160^\circ\). Since \(160^\circ
eq 180^\circ\), these cannot be angle measures of a triangle.

Answer:

Angles	Can be angle measures of a triangle	Cannot be angle measures of a triangle
(b) \(53^\circ, 125^\circ, 23^\circ\)	∘	\(\boldsymbol{\circ}\)
(c) \(15^\circ, 15^\circ, 150^\circ\)	\(\boldsymbol{\circ}\)	∘
(d) \(90^\circ, 40^\circ, 30^\circ\)	∘	\(\boldsymbol{\circ}\)