Chapter 7.3, Problem 8PSB

Solution

a.

Sum of the measures of the angles of the polygon formed.

The sum of the measures of the angles of the polygon formed is $1800$

Given: On a clock, a segment is drawn connecting the mark at the $12$ and $1$ another segment connecting the mark at $1$ and the $2$ .

Concept used: Here, we are using the formula:

Sum of angles = ${180}^{\circ }(n-2)$

Calculation: Here, the formula is sum of angles = ${180}^{\circ }(n-2)$

Here, $n=12$

Now, putting the value of n in the above formula,

➔ ${180}^{\circ }\left(12-2\right)$

➔ ${180}^{\circ }(10)$

➔ $1800$

Conclusion: Hence, the sum of the measures of the angles of the polygon formed is $1800$

b.

The sum of the measures of the exterior angles.

The sum of the measures of the exterior angles is ${360}^{\circ }$

Given: On a clock, a segment is drawn connecting the mark at the $12$ and $1$ another segment connecting the mark at $1$ and the $2$ .

Explanation: The sum of the exterior angles of a regular polygon will always equal ${360}^{\circ }$

Conclusion: Hence, the sum of the measures of the exterior angles is ${360}^{\circ }$