Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
Since triangle ABC is congruent to triangle PQR, this means that the corresponding angles will have the same measure.
Therefore, mangleB = mangleQ.
We are given that mangleB = 3v + 4, and mangleQ = 8v - 6.
Equating these expressions, we have:
3v + 4 = 8v - 6
Adding 6 to both sides:
3v + 10 = 8v
Subtracting 3v from both sides:
10 = 5v
Dividing both sides by 5:
v = 2
Substituting this value of v back into the expressions for mangleB and mangleQ:
mangleB = 3(2) + 4 = 10
mangleQ = 8(2) - 6 = 10
Therefore, mangleB = 10 and mangleQ = 10.