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
Jim G.
Feb 25, 2018

#p=4#

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#

Related questions
Impact of this question
506 views around the world
You can reuse this answer
Creative Commons License