# 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 $$\displaystyle{m}∠{C}=√∘​$$

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°

### Relevant Questions

How would you find m A. Add 30∘ to 180∘
B. Subtract 60∘ from 180∘
C. Subtract 30∘ from 90∘
D. Subtract 180∘ from 60∘.
[Triangle]
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$$\displaystyle{8}\frac{{3}}{{4}}{c}{m}$$