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Find x and Y

Thank you so much!

Find x and Y Thank you so much!-example-1
User Just Eric
by
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1 Answer

5 votes

Answer:

x = 6

y = 119

Step-by-step explanation:

Angle Relationships

When given two parallel lines with a transversal intersecting them, the angles that they create have multiple special relationships.

In the given question, we are given three angles:

  • 7x + 16
  • y + 3
  • 9x + 4

∠(7x + 16)° and ∠(y + 3)° are supplementary angles, meaning they have a sum of 180 degrees. They are neighbouring angles on the same side of the transversal.

∠(y + 3)° and ∠(9x + 4)° are also supplementary angles, as they are neighbouring angles on opposite sides of the transversal and the same side of one of the parallel lines.

Moreover, ∠(7x + 16)° and ∠(9x + 4)° are equal.

All we need is 2 equations from the above information to solve for y and x. Let's use the pair of supplementary angles:

7x + 16 + y + 3 = 180

y + 3 + 9x + 4 = 180

Combine like terms:

7x + 16 + y + 3 = 180

7x + y = 161

y + 3 + 9x + 4 = 180

y + 9x = 173

Use substitution to solve for x:

y + 9x = 173

y = 173 - 9x

7x + (173 - 9x) = 161

-2x + 173 = 161

-2x = -12

x = 6

Solve for y:

y = 173 - 9x

y = 173 - 9(6)

y = 119

User Yomara
by
8.5k points

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