Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.

Answer 1

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.