Question

1. first, choose the \angle\ tool under the \measure\ menu. (if you dont see the \measure\ menu, click \more\) to measure an angle, you must select the \angle\ tool, then click on the three points that make up the angle measurement will appear in the angle. measure each of the six angles in the regular hexagon. what is the measure of each of the six angles? a. 60 b. 100 c. 120 d. 160 8. next, we want to find the angle bisector of each angle. click on \angle bisector\ under the \construct\ menu. to find the angle bisector, you must click on the three points that make up the angle (in order). find the angle bisector for each of the six angles. what do you notice about the angle bisectors of each angle? a. the bisectors cut the angles in half b. the bisectors are perpendicular c. the bisectors are always obtuse d. the bisectors do not have any relationship with the angle

Explanation:

Question 7

Step1: Recall formula for interior angle of regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). For a regular hexagon, \( n = 6 \).

Step2: Substitute \( n = 6 \) into the formula

\[

$$\begin{align*} \frac{(6 - 2)\times180^{\circ}}{6}&=\frac{4\times180^{\circ}}{6}\\ &=\frac{720^{\circ}}{6}\\ & = 120^{\circ} \end{align*}$$

\]

An angle bisector is defined as a line that divides an angle into two equal (congruent) angles. So, by the definition of an angle bisector, it should cut the angle in half. Option B is incorrect as there's no reason for bisectors of hexagon angles to be perpendicular. Option C is incorrect as bisecting a \( 120^{\circ} \) angle gives \( 60^{\circ} \) angles (acute), not always obtuse. Option D is incorrect as the bisector has a clear relationship (dividing the angle).

Answer:

C. 120

Question 8