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
(a) 40°, 55°, 85° | ○ | ○
(b) 32°, 35°, 23° | ○ | ○
(c) 120°, 18°, 42° | ○ | ○
(d) 48°, 52°, 54° | ○ | ○

Explanation:

Step1: Recall triangle angle sum property

The sum of the interior angles of a triangle is always \(180^\circ\). For each set of angles, we will calculate their sum and check if it equals \(180^\circ\).

Step2: Analyze set (a)

Angles: \(40^\circ\), \(55^\circ\), \(85^\circ\)
Sum: \(40 + 55 + 85 = 180^\circ\)
Since the sum is \(180^\circ\), these can be angle measures of a triangle.

Step3: Analyze set (b)

Angles: \(32^\circ\), \(35^\circ\), \(23^\circ\)
Sum: \(32 + 35 + 23 = 90^\circ\)
Since \(90^\circ
eq180^\circ\), these cannot be angle measures of a triangle.

Step4: Analyze set (c)

Angles: \(120^\circ\), \(18^\circ\), \(42^\circ\)
Sum: \(120 + 18 + 42 = 180^\circ\)
Since the sum is \(180^\circ\), these can be angle measures of a triangle.

Step5: Analyze set (d)

Angles: \(48^\circ\), \(52^\circ\), \(54^\circ\)
Sum: \(48 + 52 + 54 = 154^\circ\)
Since \(154^\circ
eq180^\circ\), these cannot be angle measures of a triangle.

Answer:

(a) Can be angle measures of a triangle (select the circle under "Can be angle measures of a triangle")
(b) Cannot be angle measures of a triangle (select the circle under "Cannot be angle measures of a triangle")
(c) Can be angle measures of a triangle (select the circle under "Can be angle measures of a triangle")
(d) Cannot be angle measures of a triangle (select the circle under "Cannot be angle measures of a triangle")