Question

Question included in the image - geometry problem.

Answer 1

Answer:

y = 116°

Step-by-step explanation:

Given that L₁ || L₂:

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.  

Also, ∠y° and ∠2x° are same-side interior angles formed by the intersection of the hypotenuse of the triangle that acts as a transversal to the parallel lines, L₁ and L₂.  Given that ∠y° and ∠2x° are same-side interior angles, then it means that they are the supplements of each other, such that the sum of their measures is 180°.  

Now that we have established these definitions, we can proceed with the solution.

Equation 1:  ∠y° + ∠2x° = 180° ⇒ Same-side interior angles

Equation 2:  ∠y° =  ∠x° + ∠84°  ⇒ exterior angle theorem

Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:

∠y° + ∠2x° = 180°

∠x° +  ∠84° + 2x° = 180°

Combine like terms:

∠3x° + ∠84° = 180°

Subtract ∠84° from both sides:

∠3x° + ∠84° - ∠84° = 180° -∠84°

∠3x° = 180° - ∠84°

∠3x° = 96°

Divide both sides by 3 to solve for x:

$\frac{3x}{3} = \frac{96}{3}$

∠x° = 32°

Substitute the value of x into Equation 2 to solve for y:

∠y° =  ∠x° + ∠84°

∠y° =  ∠32° + ∠84°

∠y° =  116°

Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:

Equation 1:

∠y° + ∠2x° = 180°

116° + 2(32)° = 180°

116° + 64° = 180°

180° = 180° (True statement).

Equation 2:

∠y° =  ∠x° + ∠84°

116° = 32° + 84°

116°  = 116°  (True statement)

Therefore, the correct answer is: y = 116°.