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) 42°, 56°, 34° | ○ | ○
(b) 45°, 65°, 70° | ○ | ○
(c) 14°, 33°, 43° | ○ | ○
(d) 34°, 110°, 36° | ○ | ○

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For each set, add the angles.

Step2: Check set (a)

Sum: \(42^\circ + 56^\circ + 34^\circ = 132^\circ\). \(132
eq180\), so cannot.

Step3: Check set (b)

Sum: \(45^\circ + 65^\circ + 70^\circ = 180^\circ\). So can.

Step4: Check set (c)

Sum: \(14^\circ + 33^\circ + 43^\circ = 90^\circ\). \(90
eq180\), so cannot.

Step5: Check set (d)

Sum: \(34^\circ + 110^\circ + 36^\circ = 180^\circ\). So can.

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

(For the table, mark (a) in "Cannot", (b) in "Can", (c) in "Cannot", (d) in "Can")