Question

solve for x in this figure. enter your answer in the box. x = □°

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. Here, $n = 5$, so the sum of interior angles is $(5 - 2)\times180^{\circ}=540^{\circ}$.

Step2: Set up an equation

We know the angles of the pentagon are $90^{\circ}$ (the right - angle), $107^{\circ}$, $144^{\circ}$, $138^{\circ}$ and $x^{\circ}$. So, $90 + 107+144 + 138+x=540$.

Step3: Simplify the left - hand side

$90+107 + 144+138=479$. The equation becomes $479+x = 540$.

Step4: Solve for $x$

Subtract 479 from both sides: $x=540 - 479$.

Answer:

$x = 61$