Question

7-98. $angle a$, $angle b$, and $angle c$ are exterior angles of the triangle at right. find $mangle a$, $mangle b$, and $mangle c$. then find $mangle a + mangle b + mangle c$.
hint:
how do the angles within a triangle relate to each other? how do the exterior angles relate to those within the triangle?

Explanation:

Step1: Find interior angle for $\angle c$

First, calculate the unknown interior angle of the triangle. The sum of interior angles in a triangle is $180^\circ$.
$180^\circ - 48^\circ - 72^\circ = 60^\circ$

Step2: Calculate $m\angle a$

$\angle a$ is supplementary to $48^\circ$.
$m\angle a = 180^\circ - 48^\circ = 132^\circ$

Step3: Calculate $m\angle b$

$\angle b$ is supplementary to $72^\circ$.
$m\angle b = 180^\circ - 72^\circ = 108^\circ$

Step4: Calculate $m\angle c$

$\angle c$ is supplementary to the $60^\circ$ interior angle.
$m\angle c = 180^\circ - 60^\circ = 120^\circ$

Step5: Sum the exterior angles

Add the measures of the three exterior angles.
$m\angle a + m\angle b + m\angle c = 132^\circ + 108^\circ + 120^\circ$

Answer:

$m\angle a = 132^\circ$, $m\angle b = 108^\circ$, $m\angle c = 120^\circ$
$m\angle a + m\angle b + m\angle c = 360^\circ$