Question

for each set of three measures, determine if they can be angle measures of a triangle.
(a) (85^{circ}, 75^{circ}, 20^{circ})
(b) (58^{circ}, 34^{circ}, 42^{circ})
(c) (10^{circ}, 132^{circ}, 38^{circ})
(d) (32^{circ}, 42^{circ}, 16^{circ})

Explanation:

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For each set of angles \((a,b,c)\), we calculate \(a + b + c\) and check if it equals \(180^{\circ}\).

Step2: Check set (a)

Calculate \(85^{\circ}+75^{\circ}+20^{\circ}\)

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Step3: Check set (b)

Calculate \(58^{\circ}+34^{\circ}+42^{\circ}\)

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Step4: Check set (c)

Calculate \(10^{\circ}+132^{\circ}+38^{\circ}\)

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Step5: Check set (d)

Calculate \(32^{\circ}+42^{\circ}+16^{\circ}\)

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Answer:

(a) Can 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.