Question

Find x and y. Give reasons to justify your solution.

Answer 1

x = 36

y = 22

Explanation:

Let's solve for x

<EOG is a right angle due to the marking. Since that's the case, m<EOG = 90.

<EOF + <FOG = <EOG

Now let's substitute the values in.

54 + x = 90

x = 36

Let's solve for y

<AOB is 180 because it's a line.

<BOD + <COB = 180 because of supplementary angles

<BOD + 156 = 180

<BOD = 24

Let's create the equation now.

<AOE + <EOF + <FOG + <GOD + <BOD = <AOB

Now let's substitute the values in.

y + 54 + x + 2y + 24 = 180

3y + x + 78 = 180

Now let's substitute 36 for x.

4y + 36 + 78 = 180

3y + 114 = 180

3y = 66

y = 22

Hope this helped! If not, please let me know! <3