In the figure above, if a:b:c = 3:4:1, what is the value of a?

The line is divided up into 3 parts, a part of 3, a part of 4, and a part of 1. If we had those parts together we get 8 meaning if we divided the line into equal parts that also fit into a, b, and c there would be 8. We can than divide the line into 8 parts which would be 10 each since a line is 180 degrees. Since a is 3 than a gets 3 of those parts meaning a would be 30

I hope this helps and please don't hesitate to ask if there is anything still unclear!

jdoe0001 jdoe0001 · Answer 2 · 2019-08-22T23:55:24+02:00

let's bear in mind that a flat-line has 180°°, therefore a + b + c = 180.

now, that total of 180 is split in a ratio of 3:4:1, what we do to get the values is simply divide the total by (3+4+1) and distribute accordingly.

[tex]\bf \stackrel{a}{3\cdot \frac{180}{3+4+1}}~~:~~\stackrel{b}{4\cdot \frac{180}{3+4+1}}~~:~~\stackrel{c}{1\cdot \frac{180}{3+4+1}}\implies~\hfill \stackrel{a}{3\cdot \cfrac{45}{2}}~~:~~\stackrel{b}{4\cdot \cfrac{45}{2}}~~:~~\stackrel{c}{1\cdot \cfrac{45}{2}} \\\\\\ \stackrel{a}{\cfrac{135}{2}}~~:~~\stackrel{b}{90}~~:~~\stackrel{c}{\cfrac{45}{2}}\qquad \qquad \boxed{a = 67.5^o}[/tex]