Question

What are the missing measures?
fifty degrees, one hundred degrees

seventy-five degrees, one hundred fifty degrees

one hundred twenty-two degrees, one hundred eighty-three degrees

one hundred degrees, one hundred fifty degrees

Answer 1

do you know the formula to find the angle sum in a polygon?

Answer 2

Is it a^2 + b^2 = c^2

Answer 3

The angle sum in a triangle is 180°
the angle sum in a quadrilateral(like a square) is 360°

Answer 4

The sum of angles in a n-gon is\[(n-2)\times180°\]where n is the number of sides

Answer 5

Ok, so in this equation, we would set it up like this?

(6 - 2) x 180

Answer 6

your diagram is of a hexagon {6-gon}

Answer 7

yeah you would solve that expression
(6 - 2) x 180 and set it equal to the sums of the angles

\[(6-2)\times180°=135°+115°+120°+3x°+100°+2x°\]
now just simplify the equation and solve for
x

Answer 8

Im kinda lost..

Answer 9

ok
do the left hand side first
\[(6-2)\times180°\]

Answer 10

(6 - 2) x 180
4 X 180 = 720

Answer 11

720° good work

Answer 12

Ok now what?

Answer 13

now right hand side
\[135°+115°+120°+3x°+100°+2x°=\]

Answer 14

keep the x's seperate

Answer 15

This is where I get stuck, could you solve that part and explain how you did it?

Answer 16

\[135°+115°+120°+3x°+100°+2x°\]\[=135+115°+120°+100°+3x°+2x°\]\[=250°+220°+5x°\]\[=470°+5x°\]

Answer 17

now equate the two sides
\[720°=470°+5x°\]
now, take away 470° from both sides

Answer 18

Ok I took 470 from both sides and got 250

Answer 19

that is right so far then
250°=5x°
you can divide both sides by 5

Answer 20

250/ 5 = 50

Answer 21

so x= 50°,
now your question is asking for the missing angles
ie 2x and 3x

Answer 22

Ok so do I multiply 2 times 50 and 3 time 50?

Answer 23

yes, 2 times 50 is one angle measure and the other is 3 times 50

Answer 24

Ok Thank you SOOOOO MUCHHH!! Your an amazing math helper!

Answer 25

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