Chapter 7.3, Problem 10PSB

Solution

a.

To find: The number of the sides of polygon if the sum of its angles is ${900}^o$ .

The sides of the polygon are $7$ .

Given: The sum of measure of its angles is $900$

Concept used: Here, we are using the formula:

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

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

Now, $900={180}^{\circ }(n-2)$

➔ $900=180n-360$

➔ $1260=180n$

➔ $n=7$

Conclusion: Hence, the sides of the polygon are $7$ .

b.

To find: The number of the sides of polygon if the sum of its angles is ${1440}^o$

The sides of the polygon if the sum is $1440$ are $10$

Given: The sum of measure of its angles is $1440$

Concept used: Here, we are using the formula:

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

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

Now, $1440={180}^{\circ }(n-2)$

➔ $1440=180n-360$

➔ $1800=180n$

➔ $n=10$

Conclusion: Hence, the sides of the polygon if the sum is $1440$ are $10$

c.

To find: The number of the sides of polygon if the sum of its angle is ${2880}^o$ .

The sides of the polygon $2880$ are $18$

Given: The sum of measure of its angles is $2880$

Concept used: Here, we are using the formula:

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

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

Now, $2880={180}^{\circ }(n-2)$

➔ $2880=180n-360$

➔ $3240=180n$

➔ $n=18$

Conclusion: Hence, the sides of the polygon are $18$

d.

To find: The number of the sides of polygon if the sum of its angle is $180x-720$ .

The sides of the polygon are $x+2$

Given: The sum of measure of its angles is $180x-720$

Concept used: Here, we are using the formula:

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

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

Now, $180x-720={180}^{\circ }(n-2)$

➔ $x-4=n-2$

➔ $x-n=2$

➔ $n=x+2$

Conclusion: Hence, the sides of the polygon are $x+2$

e.

To find: The number of the sides of polygon if the sum of its angle is ${436}^o$ .

The sides of the polygon are $4.22$ which is not possible.

Given: The sum of measure of its angles is $436$

Concept used: Here, we are using the formula:

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

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

Now, $436={180}^{\circ }(n-2)$

➔ $436=180n-360$

➔ $796=180n$

➔ $n=4.22$

Conclusion: Hence, the number of the sides of the polygon if the sum is $436$ are $4.22$ which is not possible.

f.

To find: The number of the sides of polygon if the sum of its angles is equal to six right angles.

The sides of the polygon if the sum is $540$ are $5$

Given: The sum of measure of its angles is $540$

Concept used: Here, we are using the formula:

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

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

Now, $540={180}^{\circ }(n-2)$

➔ $540=180n-360$

➔ $900=180n$

➔ $n=5$