Answer :

Answer:

x = 9 , y = 8

Step-by-step explanation:

Given Δ HJK and Δ TRS are congruent , then corresponding angles are congruent.

∠ T = ∠ H , that is

6x - 3 = 51 ( add 3 to both sides )

6x = 54 ( divide both sides by 6 )

x = 9

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and

∠ K = ∠ S

using the sum of the 3 angles in a Δ is 180°

∠ S = 180° - ∠ R - ∠ T = 180° - 51° - 83° = 180° - 134° = 46° , so

7y - 10 = 46 ( add 10 to both sides )

7y = 56 ( divide both sides by 7 )

y = 8

Heather

Answer: x = 9 and y = 8, or (9, 8)

Step-by-step explanation:

     It is given that these two triangles are congruent, so their angle measurements must be congruent as well. This means that m∠H = m∠T, m∠J = m∠R, and m∠K = m∠S. With this information, we can create an equation to solve for x.

           Given:

           m∠H = m∠T

           Substitute expressions for angles:

           51 = 6x - 3

           Add 3 to both sides of the equation:

           54 = 6x

           Divide both sides of the equation by 6:

           [tex]\boxed{x = 9}[/tex]

     To solve for y, we must remember that a triangle's interior angles add up to 180 degrees. We can substitute the value of x that we found to find y.

           Given:

           m∠K = m∠S

           Substitute expressions for angles:

           7y - 10 = 180 - (6x - 3 + 83)

           Distribute the -1:

           7y - 10 = 180 - 6x + 3 - 83

           Combine like terms:

           7y - 10 = 100 - 6x

           Add 10 to both sides of the equation and substitute 9 for x:

           7y = 100 - 6(9) + 10

           Add 10 to 100 and multiply 6 by 9:

           7y = 110 - 54

           Subtract:

           7y = 56

           Divide both sides of the equation by 7:

           [tex]\boxed{y = 8}[/tex]

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