Question

determining angle measures
let $m\angle a = 40^\circ$. if $\angle b$ is a complement of $\angle a$, and $\angle c$ is a supplement of $\angle b$, find these measures.
$m\angle b = \square^\circ$
$m\angle c = \square^\circ$

Explanation:

Step1: Find $m\angle B$ (complement)

Complementary angles sum to $90^\circ$.
$m\angle B = 90^\circ - m\angle A = 90^\circ - 40^\circ$

Step2: Calculate $m\angle B$

$m\angle B = 50^\circ$

Step3: Find $m\angle C$ (supplement)

Supplementary angles sum to $180^\circ$.
$m\angle C = 180^\circ - m\angle B = 180^\circ - 50^\circ$

Step4: Calculate $m\angle C$

$m\angle C = 130^\circ$

Answer:

$m\angle B = 50^\circ$
$m\angle C = 130^\circ$