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) 51°, 133°, 124°
(b) 15°, 150°, 15°
(c) 35°, 102°, 62°
(d) 30°, 90°, 40°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is always 180°.

Step2: Calculate sum for (a)

$51^{\circ}+133^{\circ}+124^{\circ}=308^{\circ}
eq180^{\circ}$

Step3: Calculate sum for (b)

$15^{\circ}+150^{\circ}+15^{\circ}=180^{\circ}$

Step4: Calculate sum for (c)

$35^{\circ}+102^{\circ}+62^{\circ}=199^{\circ}
eq180^{\circ}$

Step5: Calculate sum for (d)

$30^{\circ}+90^{\circ}+40^{\circ}=160^{\circ}
eq180^{\circ}$

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) Cannot be angle measures of a triangle