Question

1. five angles of a hexagon measure 110°. what is the measure of the remaining angle?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \). For a hexagon, \( n = 6 \). So we calculate the sum of interior angles:
\( S=(6 - 2)\times180^{\circ}=4\times180^{\circ} = 720^{\circ} \)

Step2: Calculate the sum of the five given angles.

Each of the five angles is \( 110^{\circ} \), so the sum of these five angles is \( 5\times110^{\circ}=550^{\circ} \)

Step3: Find the measure of the remaining angle.

Let the measure of the remaining angle be \( x \). We know that the sum of all six interior angles is \( 720^{\circ} \), so \( 550^{\circ}+x = 720^{\circ} \). Solving for \( x \), we get \( x=720^{\circ}- 550^{\circ}=170^{\circ} \)

Answer:

The measure of the remaining angle is \( 170^{\circ} \)