Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
Since the triangles are congruent, the corresponding angles are congruent. We are given that m∠B = 3v + 4 and m∠Q = 8v - 6.
So, m∠B = m∠Q.
Therefore, 3v + 4 = 8v - 6.
To solve for v, we can subtract 3v from both sides and add 6 to both sides.
3v - 3v + 4 + 6 = 8v - 3v - 6 + 6.
10 = 5v.
To solve for v, we can divide both sides by 5.
10/5 = v.
2 = v.
Now that we have the value of v, we can substitute it back into the expressions for m∠B and m∠Q.
m∠B = 3v + 4 = 3(2) + 4 = 6 + 4 = 10.
m∠Q = 8v - 6 = 8(2) - 6 = 16 - 6 = 10.
So, m∠B = 10 and m∠Q = 10.