Question

explore solving for an angle measure of a polygon
visit to bit.ly/30hs7nn or scan the qr code to the right for an interactive tool to investigate this exploration (adapted from lesson 1.2).
work with your teacher/tutor. the sum s of the angle measures of a polygon with n sides can be found using the formula s = 180(n - 2). write and solve an equation to find each value of x. justify the steps in your solution. the first one is done for you.
a)
this figure has a sides so the sum of angles is given by:
s = 180(3 - 2)
n = 3
s = 180×1 = 180
30+(30 + x)+9x = 180
60+10x = 180
10x = 180 - 60 = 120
x = 120/10 = 12
b)
this figure has b sides so the sum of angles is given by:
s = 180(4 - 2)
n = 4
s = 180×2 = 360
50+(2x + 30)+(2x + 20)+x = 360
100+5x = 360
5x = 360 - 100 = 260
x = 260/5 = 52
use the angle measurement tool to measure the angles of each polygon. do the angle measures agree with your results?
page 13
integrated math 1 a credit 1

Explanation:

Step1: Determine number of sides for polygon A

The polygon in part A is a triangle, so $n = 3$.

Step2: Calculate sum of interior - angles for polygon A

Using the formula $S=180(n - 2)$, when $n = 3$, we have $S=180\times(3 - 2)=180^{\circ}$.

Step3: Set up an equation for polygon A

The sum of the angle measures in the triangle is $30+(30 + x)+9x=180$. Combine like - terms: $60 + 10x=180$.

Step4: Solve the equation for polygon A

Subtract 60 from both sides: $10x=180 - 60=120$. Then divide both sides by 10: $x = 12$.

Step5: Determine number of sides for polygon B

The polygon in part B is a quadrilateral, so $n = 4$.

Step6: Calculate sum of interior - angles for polygon B

Using the formula $S = 180(n - 2)$, when $n = 4$, we have $S=180\times(4 - 2)=360^{\circ}$.

Step7: Set up an equation for polygon B

The sum of the angle measures in the quadrilateral is $50+(2x + 30)+(2x + 20)+x=360$. Combine like - terms: $100+5x=360$.

Step8: Solve the equation for polygon B

Subtract 100 from both sides: $5x=360 - 100=260$. Then divide both sides by 5: $x = 52$.

Answer:

For polygon A, $x = 12$. For polygon B, $x = 52$.