Question

One angle of a decagon is ${90}^{\circ }$ and all the remaining nine angles are equal. What is the measure of the other angles?

Answer 1

One angle of the decagon $=$ ${90}^{\circ }$
The number of sides $\left(n\right)=10$
The sum of interior angles $=(2n-4)$ x ${90}^{\circ }$
Let each of the other angles be equal to $x^{\circ }$
$9x+{90}^{\circ }=(20-4)\times {90}^{\circ }=16\times {90}^{\circ }={1440}^{\circ }$
$9x=1440-{90}^{\circ }={1350}^{\circ }$
$x=\frac{{1350}^{\circ }}{9}={150}^{\circ }$

Each of the other angles $={150}^{\circ }$