Answer
The value of $x$ is $126^{\circ}$,
Angle measures are $126^{\circ},126^{\circ},96^{\circ},96^{\circ},96^{\circ}$
Work Step by Step
Sum of angle measures is $540^{\circ}$.
Add all the given angle.
$=(x-30)^{\circ}+(x-30)^{\circ}+(x-30)^{\circ}+x^{\circ}+x^{\circ}$
Equate both values.
$\Rightarrow (x-30)^{\circ}+(x-30)^{\circ}+(x-30)^{\circ}+x^{\circ}+x^{\circ} =540^{\circ} $
Clear the parentheses.
$\Rightarrow x^{\circ}-30^{\circ}+x^{\circ}-30^{\circ}+x^{\circ}-30^{\circ}+x^{\circ}+x^{\circ} =540^{\circ} $
Add like terms.
$\Rightarrow 5x^{\circ}-90^{\circ}=540^{\circ} $
Add $90^{\circ}$ to each side.
$\Rightarrow 5x^{\circ}-90^{\circ}+90^{\circ}=540^{\circ} +90^{\circ}$
Simplify.
$\Rightarrow 5x^{\circ}=630^{\circ}$
Divide each side by $5$.
$\Rightarrow \frac{5x^{\circ}}{5}=\frac{630^{\circ}}{5}$
Simplify.
$\Rightarrow x^{\circ}=126^{\circ}$
Angle measures are
$=(x-30)^{\circ}=(126-30)^{\circ}=96^{\circ}$
Hence, the value of $x$ is $126^{\circ}$ and angle measures are $126^{\circ},126^{\circ},96^{\circ},96^{\circ},96^{\circ}$.
