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
-------------------------------------------------------------
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
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]