Chapter 7.3, Problem 1PSA

Solution

a.

The sum of the measures of the angles of quadrilateral.

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

Given: Quadrilateral

Concept used: Here, we are using the formula:

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

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

By putting the value of n = $4$ in the given formula, we get

➔ ${180}^{\circ }(4-2)$

➔ ${360}^{\circ }$

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

b.

The sum of the measures of the angles of a heptagon

The sum of the measures of the angles of heptagon is ${900}^{\circ }$

Given: Heptagon

Concept used: Here, we are using the formula:

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

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

By putting the value of n = $7$ in the given formula, we get

➔ ${900}^{\circ }$

Conclusion: Hence, the sum of the measures of the angles of heptagon is ${900}^{\circ }$

c.

The sum of the measures of the angles of an octagon.

The sum of the measures of the angles of octagon is ${1080}^{\circ }$

Given: Octagon

Concept used: Here, we are using the formula:

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

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

By putting the value of n = $8$ in the given formula, we get

➔ ${180}^{\circ }(8-2)$

➔ ${1080}^{\circ }$

Conclusion: Hence, the sum of the measures of the angles of octagon is ${1080}^{\circ }$

d.

The sum of the measures of the angles of a dodecagon.

The sum of the measures of the angles of dodecagon is ${1800}^{\circ }$

Given: Dodecagon

Concept used: Here, we are using the formula:

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

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

By putting the value of n = $12$ in the given formula, we get

➔ ${180}^{\circ }(12-2)$

➔ ${1800}^{\circ }$

Conclusion: Hence, the sum of the measures of the angles of dodecagon is ${1800}^{\circ }$

e.

The sum of the measures of the angles of a- $93$ gon

The sum of the measures of the angles of a- $93$ gon is ${16380}^{\circ }$

Given: A- $93$ gon

Concept used: Here, we are using the formula:

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

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

By putting the value of n = $93$ in the given formula, we get

➔ ${180}^{\circ }(93-2)$

➔ ${16380}^{\circ }$

Conclusion: Hence, the sum of the measures of the angles of a- $93$ gon is ${16380}^{\circ }$