Question

what is the sum of all the angles that are labeled? 72° 36°

Explanation:

Step1: Identify the labeled angles

The labeled angles are $72^{\circ}$, $36^{\circ}$ and $x^{\circ}$. Since the angles around a point sum to $360^{\circ}$, and we assume the un - labeled part of the circle is a straight line (angle of $180^{\circ}$), we first find $x$. We know that $x + 72+36=180$ (for the semi - circle part). So $x=180-(72 + 36)$.
$x=180 - 108=72^{\circ}$

Step2: Calculate the sum of labeled angles

The sum of the labeled angles is $72+36 + 72$.
$72+36+72=180^{\circ}$

Answer:

$180^{\circ}$