Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
Responses
22
22
11
11
10
10
25
To determine the values of angle B and angle Q, we can equate their expressions.
m∠B = 3v + 4
m∠Q = 8v – 6
Since triangle ABC is congruent to triangle PQR, the corresponding angles are equal. Therefore, we can set up the following equation:
3v + 4 = 8v – 6
To solve for v, let's isolate the variable terms on one side:
3v - 8v = -6 - 4
-5v = -10
Dividing both sides by -5:
v = 2
Now that we have the value for v, we can substitute it back into the expressions for angle B and angle Q to find their specific values.
m∠B = 3(2) + 4
m∠B = 6 + 4
m∠B = 10
m∠Q = 8(2) – 6
m∠Q = 16 – 6
m∠Q = 10
Therefore, angle B is 10 degrees and angle Q is also 10 degrees. The correct answer is:
10
10