Question

: concepts and connections (27.0821000) yl ic (spring)
complementary and supplementary angles
assignment active
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: Calculate complement of ∠A

Complementary angles sum to $90^\circ$. So $m\angle B = 90^\circ - m\angle A$
$m\angle B = 90^\circ - 40^\circ = 50^\circ$

Step2: Calculate supplement of ∠B

Supplementary angles sum to $180^\circ$. So $m\angle C = 180^\circ - m\angle B$
$m\angle C = 180^\circ - 50^\circ = 130^\circ$

Answer:

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