Question

if 4 of the angles of a pentagon sum to 470°, what is the measure of the 5th angle?
70°
90°
130°
180°

Explanation:

Step1: Recall sum of interior angles of pentagon

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

Step2: Find the fifth - angle

Let the measure of the fifth angle be $x$. We know that the sum of 4 angles is $470^{\circ}$, and the sum of all 5 angles is $540^{\circ}$. So, $x=540^{\circ}-470^{\circ}$.
$x = 70^{\circ}$

Answer:

A. $70^{\circ}$