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A convex quadrilateral has exterior angle measures, one at each vertex, of 5b+7°, 34b–33°, b+36°, and 37b–35°. What is the value of b?

Answer 1

Sadie Allen

#b=5#

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

#"the sum of the 4 exterior angles is then"#

#5b+7+34b-33+b+36+37b-35=360#

#rArr77b-25=360#

#"add 25 to both sides"#

#77bcancel(-25)cancel(+25)=360+25#

#rArr77b=385#

#"divide both sides by 77"#

#(cancel(77) b)/cancel(77)=385/77#

#rArrb=5#

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Answer 2

Maverick Smith

#b = 5^@#.

As soon as I read the question and it was talking about exterior angles I wrote the values above are equal to #360^@#.

#5b+7 + 34b - 33 + b + 36 + 37b - 35 = 360^@#

It equals #360^@# as exterior angles add up to #360^@# as it goes all around a point. So when you simplify the values give you get

#77b - 25 = 360 #

#77b = 360 + 25#

#77b= 385#

Divide both sides by #77# to isolate #b#

#b= 5#

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Answer from HIX Tutor

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