If △XYZ ≅ △RST, m∠X = 25, m∠Z = 65, and m∠S = 12x + 6, find the value of x.
12x + 6 = 180 - 25 - 65
solve for x
To find the value of x, we need to compare the corresponding angles of the congruent triangles △XYZ and △RST. From the given information, we know that ∠X is congruent to ∠R, ∠Y is congruent to ∠S, and ∠Z is congruent to ∠T.
Given that m∠X = 25, and △XYZ ≅ △RST, we can conclude that m∠R = 25.
Similarly, given that m∠Z = 65, and △XYZ ≅ △RST, we can conclude that m∠T = 65.
Now, we need to find the value of x using the third pair of corresponding angles. We know that m∠S = 12x + 6, and △XYZ ≅ △RST. Therefore, m∠Y = m∠S.
Since ∠Y is congruent to ∠S, we have:
m∠Y = m∠S
12x + 6 = m∠Y
And since ∠Y is congruent to ∠S, we also know that:
m∠Y = m∠S = m∠T
12x + 6 = 65
Now, we can solve for x by subtracting 6 from both sides of the equation:
12x + 6 - 6 = 65 - 6
12x = 59
Finally, divide both sides of the equation by 12 to isolate x:
12x/12 = 59/12
x = 59/12
Therefore, the value of x is 59/12.