Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
Since triangle ABC is congruent to triangle PQR, their corresponding angles are congruent. Therefore, we have the following equation:
m<B = m<Q.
Given that m<B = 3v + 4 and m<Q = 8v - 6, we can set up the equation:
3v + 4 = 8v - 6.
To solve for v, we can subtract 3v from both sides and add 6 to both sides:
4 + 6 = 8v - 3v,
10 = 5v.
Dividing both sides by 5, we get:
v = 2.
Now we can substitute v = 2 into either of the original equations to find m<B and m<Q.
Using m<B = 3v + 4, we substitute v = 2:
m<B = 3(2) + 4 = 6 + 4 = 10.
Using m<Q = 8v - 6, we substitute v = 2:
m<Q = 8(2) - 6 = 16 - 6 = 10.
Therefore, m<B = m<Q = 10.