Find the remaining angles for △ABC. m∠B=30∘ and m∠A=1/2m∠C m∠A=√∘ and m∠C=√∘​

Question
Find the remaining angles for \(\displaystyle△{A}{B}{C}\). \(\displaystyle{m}∠{B}={30}∘{\quad\text{and}\quad}{P}{S}{K}{m}∠{A}=\frac{{1}}{{2}}{m}∠{C}\)
\(\displaystyle{m}∠{A}=√∘\) and \(\displaystyle{m}∠{C}=√∘​\)

Answers (1)

2021-01-05
The sum of the angle measures of a triangle is 180° so we can write: \(\displaystyle{m}∠{A}+{m}∠{B}+{m}∠{C}={180}°\)
Substitute \(\displaystyle{m}∠={30}°{\quad\text{and}\quad}{P}{S}{K}{m}∠{A}={12}{m}∠{C}\): \(\displaystyle\frac{{1}}{{2}}{m}{<}{C}+{30}°+{m}{<}{C}={180}°\)</span>
Solve for \(\displaystyle{m}∠{C}\)
\(\displaystyle\frac{{3}}{{2}}{m}{<}{C}+{30}°={180}°\)</span>
\(\displaystyle\frac{{3}}{{2}}{m}{<}{C}={150}°\)</span>
\(\displaystyle{m}{<}{C}=\frac{{2}}{{3}}\cdot{150}°\)</span>
\(\displaystyle{m}{<}{C}={100}°\)</span>
Hence, \(\displaystyle{m}{<}{A}=\frac{{1}}{{2}}{\left({100}°\right)}\)</span>
PSKm<A=50°
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