221k views
2 votes
Does anyone know how to do this?:(

Does anyone know how to do this?:(-example-1
User KHansen
by
8.0k points

1 Answer

4 votes

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.

User Tary
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories