Question

Find the angle measure of $x$ in the following figures.

Answer 1

(a)

Sum of all interior angles of quadrilateral $={360}^0$
$\therefore 50+130+120+x=300$
$x={60}^0$

(b)

$90+a=180$
$a=90$
Sum of all angles of quad $=360$
$x+70+60+90=360$
$x={140}^0$

(c)

$70+a=180$ (Linear pair)
$a=110$
$60+b=180$ (Linear pair)
$b=120$
Sum of measures of all angles of pentagon $={540}^0$
$\therefore 120+110+x+x+30=540$
$2x=280$
$x={140}^0$

(d)

Sum of all angles of pentagon $540$
Given all angles are equal
$\therefore 5x=540$
$x={108}^0$