Question

Two angles of a quadrilateral measure ${80}^o$ each. The other two differ by ${20}^o$. What is the measure of each of the other angles.

Answer 1

Let $x$ and $y$ be the other two angles such that $x>y$.

Now,

$x-y=20°.....\left(1\right)$

Also,

$80°+80°+x+y=360°\left(\text{Sum of interior angles of a quadrilateral}\right)$

$\Rightarrow x+y=360°-160°=200°.....\left(2\right)$

Adding equation $\left(1\right)$ and $\left(2\right)$, we get

$2x=220°$

$\Rightarrow x=\frac{220°}{2}=110°$

Substituting the value of $x$ in equation $\left(1\right)$, we have

$y=x-20°=110°-20°=90°$

Hence the other angles are $90°$ and $110°$ respectively.