A convex hexagon has exterior angle measures, one at each vertex, of 30°, 2t–25°, 30°, 56°, 66°, and 3t–14°. What is the value of t?

2 Answers
Sahar Mulla ❤
Feb 25, 2018

Sum of exterior angle for any polygon is always #360^@#

#30°+ 2t–25°+ 30°+ 56°+ 66°+ 3t–14° = 360#

#5t+ 30 – 25 + 30 + 56 + 66 – 14 = 360#

#5t = 360-143=217#

#t=217/5 = 43.4#

-Sahar :)

Jim G.
Feb 25, 2018

#t=217/5#

Explanation:

#"the "color(blue)"sum of the exterior angles "=360^@#

#"sum the 6 exterior angles and equate to 360"#

#30+2t-25+30+56+66+3t-14=360#

#rArr5t+143=360#

#"subtract 143 from both sides"#

#5tcancel(+143)cancel(-143)=360-143#

#rArr5t=217#

#"divide both sides by 5"#

#(cancel(5) t)/cancel(5)=217/5#

#rArrt=217/5larrcolor(red)"exact value"#

Related questions
Impact of this question
1983 views around the world
You can reuse this answer
Creative Commons License