To find the measures of angle B and angle Q, we can set up an equation by using the congruence of the triangles.
Since triangle ABC is congruent to triangle PQR, this means that angle B is congruent to angle Q. Therefore, we can set up the equation:
m(angle B) = m(angle Q)
From the given information, we know that m(angle B) = 3v + 4 and m(angle Q) = 8v - 6.
Setting these two expressions equal to each other, we have:
3v + 4 = 8v - 6
To solve for v, we can simplify the equation by combining like terms:
4 + 6 = 8v - 3v
10 = 5v
Dividing both sides by 5:
v = 2
Now, we can substitute this value back into one of the expressions to find the measures of both angles:
m(angle B) = 3v + 4
m(angle B) = 3(2) + 4
m(angle B) = 6 + 4
m(angle B) = 10
So, angle B measures 10 degrees.
Similarly,
m(angle Q) = 8v - 6
m(angle Q) = 8(2) - 6
m(angle Q) = 16 - 6
m(angle Q) = 10
So, angle Q also measures 10 degrees.
Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
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