A convex octagon has interior angle measures of 47p–38°, 42p–18°, 150°, 148°, 36p, 35p, p+45°, and 149°. What is the value of p?
1 Answer
Feb 25, 2018
Explanation:
#"to calculate the "color(blue)"sum of the interior angles"#
#• " sum "=180^@(n-2)#
#"where n is the number of sides of the polygon"#
#"here "n=8#
#rArr"sum "=180^@xx6=1080^@#
#"sum the interior angles and simplify"#
#47p-38+42p-18+150+148+36p+35p+p+45+149#
#=161p+436#
#"equate to 1080 and solve for p"#
#161p+436=1080#
#"subtract 436 from both sides"#
#161pcancel(+436)cancel(-436)=1080-436#
#rArr161p=644#
#"divide both sides by 161"#
#(cancel(161) p)/cancel(161)=644/161#
#rArrp=4#