Question

A quadrilateral has two angles that measure 240° and 20°. The other two angles are in a ratio of 3:7. What are the measures of those two angles

Answer 1

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360`

so since a quadrilateral will have a total of 360°, minus 240 and 20 that leaves us with only 100° leftover, now to make it in a 3 : 7 ratio, let's simply divide 100 by (3 + 7) and distribute accordingly.

`3~~ : ~~7\implies 3\cdot (100)/(3+7)~~ : ~~7\cdot (100)/(3+7)\implies 3\cdot 10~~ : ~~7\cdot 10\implies 30^o~~ : ~~70^o`