Question

if anglec=angleb and anglea=4angleb, find the value of each angle.

Non-right triangles and trigonometry
ANSWERED
asked 2020-12-06
if \(\displaystyle\angle{c}=\angle{b}{\quad\text{and}\quad}\angle{a}={4}\angle{b}\), find the value of each angle.

Answers (1)

2020-12-07
The sum of all angles in any triangles is \(\displaystyle{180}^{\circ}\), so
\(\displaystyle\angle{a}+\angle{b}+\angle{c}={180}\)
Substitute \(\displaystyle\angle{c}=\angle{b}{\quad\text{and}\quad}\angle{a}={4}\angle{b}\) to solve for \(\displaystyle\angle{b}\):
\(\displaystyle{4}\angle{b}+\angle{b}+\angle{b}={180}^{\circ}\)
\(\displaystyle{6}\angle{b}={180}^{\circ}\)
\(\displaystyle\angle{b}=\frac{{{180}^{\circ}}}{{6}}\)
\(\displaystyle\angle{b}={30}^{\circ}\)
Substitute \(\displaystyle\angle{c}=\angle{b}\) to solve for \(\displaystyle\angle{c}\):
\(\displaystyle\angle{c}={30}^{\circ}\)
Substitute \(\displaystyle\angle{a}={4}\angle{b}\to\) solve for \(\displaystyle\angle{a}\):
\(\displaystyle\angle{a}={4}\times{30}^{\circ}\)
\(\displaystyle\angle{a}={120}^{\circ}\)
The answer:
\(\displaystyle\angle{b}={30}^{\circ},\angle{c}={30}^{\circ},\angle{a}={120}^{\circ},\)
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