Answer:
The size of angle AFE (or Angle F) is 162º.
Explanation:
A hexagon's angles add up to 720º. Since there is one line of symmetry (straight down the middle), angle A is the same as angle B; 117º, also known as X. This means angle F is equal to angle C, and angle E is equal to angle D. Angles A and B are to be represented by X. Angles F and C are to be represented by Y. Angles E and D are to be represented by Z. We need to find the remaining sum of the unknown angles: 720 - (117 • 2) = 486º. In the given information, angles BCD (y) is equal to 2 • angle CDE (z). In other words, y = 2z. There are 2y; to convert 2y into z's, we multiply y's equal of z by 2 to get 4z. 2y = 4z. Now we can write an equation to solve: (720 - 2x) ÷ (4z + 2z) = z. Where x is 117º. First we solve part 1:
720 - 2(117) = ?
720 - 234 = 486º
Rewrite the equation: 486 ÷ (4z + 2z) = z. That's not how I want to solve it, so I'm rewriting it again as 486 = 4z + 2z. Now to solve it:
Solve for z (Part 2):
486 = 4z + 2z
486 = 6z Combine like terms
----------------------------------------------------------------------
Long division:
081
6 |486
- 0↓
48
- 48↓
06
- 6
0
----------------------------------------------------------------------
81 = z Divide both sides by 6
Solve for y:
y = 2z
y = 2(81) Plug 81 in for z
y = 162
Checking my work:
720 = 2x + 2y + 2z
720 = 2(117) + 2(162) + 2(81) 117 = x; 162 = y; 81 = z
720 = 234 + 324 + 162 Simplify
720 = 720 Add
Woop woop!! We're almost done!
Remember the question is asking us to "work out the size of angle AFE" (or angle F for short). Angle F is represented by y, so we simply look for where we solved for y and see that y(AFE) = 162.
Hope this helps,
❤A.W.E.S.W.A.N.❤