Question

$\Delta$ABC and $\Delta$PQR are congruent triangles such that BC = 2x cm, QR = (4x - 6) cm, $\angle$P = (5y - 1)°, and $\angle$A = (2y + 11)°. Find the values of x and y.

• A. x = 1, y = 3
• B. x = 4, y = -2
• C. x = 3, y = 4
• D. x = -2, y = 1

Answer 1

The correct option is C x = 3, y = 4

Given: $\Delta$ABC $\cong$ $\Delta$PQR, BC = 2x cm, QR = (4x - 6) cm, $\angle$P = (5y - 1)°, and $\angle$A = (2y + 11)°

We know that corresponding parts of congruent triangles are equal.

$\Delta$ABC $\cong$ $\Delta$PQR, so
QR = BC
2x = 4x - 6
2x = 6
x = 3

$\angle$P = $\angle$A
5y - 1 = 2y + 11
3y = 12
y = 4