Question

In the adjoining figure, find $x+y+z+w$.

Answer 1

We know that interior angle sum of a Quadrilateral is ${360}^o$

let the missing internal angle be $p$

$p+{130}^o+{80}^o+{70}^o={360}^o\Rightarrow p={80}^o$

Also, we can see that adjacent interior and exterior angles are supplementary

$\to x+{130}^o={180}^o\Rightarrow x={50}^o$

Similarly, $y={100}^{o}z={110}^{o}w={100}^o$

Hence, $x+y+z+w={50}^o+{100}^o+{110}^o+{100}^o={360}^o$