Question

for each set of three measures, determine if they can be angle measures of a triangle.
(a) can these be the angle measures of a triangle?
$75^{\circ}$, $55^{\circ}$, $50^{\circ}$
$\circ$ yes $\circ$ no
(b) can these be the angle measures of a triangle?
$43^{\circ}$, $33^{\circ}$, $14^{\circ}$
$\circ$ yes $\circ$ no
(c) can these be the angle measures of a triangle?
$132^{\circ}$, $38^{\circ}$, $10^{\circ}$
$\circ$ yes $\circ$ no

Explanation:

Part (a)

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the sum

Sum \(= 75^\circ + 55^\circ + 50^\circ = 180^\circ\).

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the sum

Sum \(= 43^\circ + 33^\circ + 14^\circ = 90^\circ
eq180^\circ\).

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the sum

Sum \(= 132^\circ + 38^\circ + 10^\circ = 180^\circ\).

Answer:

Yes

Part (b)