Question

Please help me to find the solution

Answer 1

wowie thats one heck of a answer

Answer 2

Hey there! :D

We have all the given information.

We know that all the angles added up will equal <AOF.

So, from angle <A to angle <D it is 82 degrees. From <B to <E that is 68. The three top angles are the same measure, the bottom two are the same measure.

Let's let <AOB and <BOC stand for x, and <COD, <DOE, and <EOF stand for y.

We have two equations here.

2x+y= 82

x+2y= 68

We have to switch one thing around.

2x+y=82

Subtract 2x from that.

y=82-2x

Plug that into the other equation.

x+2(82-2x)=68

x+164-4x=68

164-3x=68

-3x= -96

x=32

Now we know that <AOB and <BOC are 32 degrees.

Now plug that in to find y.

2x+y=82

2(32)+y=82

64+y=82

y=18

Now we know the measure of all the smaller angles.

So, here's our last equation: (since we have 3 smaller angles and 2 larger ones)

18y+32x=

18(3)+32(2)= 118

<AOF= 18 degrees

I hope this helps!

~kaikers