Question

If two angles of a quadrilateral are ${40}^{\circ }$ and ${110}^{\circ }$ and the other two are in the ratio $3:4$, find these angles.

Answer 1

We know that,
Sum of all four angles of a quadrilateral = ${360}^o$
Sum of two given angles = ${40}^o+{110}^o={150}^o$
So, the sum of remaining two angles = ${360}^o-{150}^o={210}^o$
Also given,
Ratio of these angles = $3:4$
Hence,
Third angles = $\frac{3}{3+4}\times {210}^o$ = $\frac{3}{7}\times {210}^o$ = ${90}^o$

And,
Fourth angle = $\frac{4}{3+4}\times {210}^o$ = $\frac{4}{7}\times {210}^o$ = ${120}^o$