Question
Find the $\angle$ measure $x$ in the below figure.
✓
Answer
$x + 30^\circ + x + (180^\circ – 70^\circ ) + (180^\circ – 60^\circ ) = (5 – 2)$
$\times$ $180^\circ $ [ By angle sum property of a pentagon]
$\therefore$ $2x + 30^\circ + 110^\circ + 120^\circ = 540^\circ $
$\therefore$ $2x + 260^\circ = 540^\circ $
$\therefore$ $2x = 540^\circ – 260^\circ$
$\therefore$ $2x = 280^\circ $
$\therefore$ $x = \frac{{280^\circ }}{2}$
$\therefore$ $x = 140^\circ $
$\times$ $180^\circ $ [ By angle sum property of a pentagon]
$\therefore$ $2x + 30^\circ + 110^\circ + 120^\circ = 540^\circ $
$\therefore$ $2x + 260^\circ = 540^\circ $
$\therefore$ $2x = 540^\circ – 260^\circ$
$\therefore$ $2x = 280^\circ $
$\therefore$ $x = \frac{{280^\circ }}{2}$
$\therefore$ $x = 140^\circ $
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