Question

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
25

Answer 1

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.