Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
Responses
22
22
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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.
To find the values of mangleB and mangleQ, we need to set up an equation since the two triangles are congruent.
Since angle B corresponds to angle Q in the congruent triangles, we can set up an equation as follows:
mangleB = mangleQ
Given that mangleB = 3v + 4 and mangleQ = 8v - 6, we can substitute these values into the equation:
3v + 4 = 8v - 6
Next, we can solve for v by isolating it on one side of the equation:
3v - 8v = -6 - 4
-5v = -10
Finally, we can solve for v:
v = -10 / -5
v = 2
Now that we know the value of v, we can substitute it back into the equations to find the measures of angle B and angle Q.
mangleB = 3v + 4
mangleB = 3(2) + 4
mangleB = 6 + 4
mangleB = 10
mangleQ = 8v - 6
mangleQ = 8(2) - 6
mangleQ = 16 - 6
mangleQ = 10
Therefore, the measures of angle B and angle Q are both 10. Hence, the correct answer is:
mangleB = 10
mangleQ = 10
To find the measure of angle B and angle Q, you need to set the measures of angle B and angle Q equal to each other and solve for v.
First, set up the equation: m∠B = m∠Q.
This can be written as:
3v + 4 = 8v - 6.
Now, solve for v by isolating it on one side of the equation:
Subtract 3v from both sides:
4 = 5v - 6.
Add 6 to both sides:
10 = 5v.
Divide both sides by 5:
v = 2.
Now that you have found the value of v, you can substitute it back into the original equations to find the measures of angle B and angle Q.
For angle B:
m∠B = 3v + 4 = 3(2) + 4 = 6 + 4 = 10.
For angle Q:
m∠Q = 8v - 6 = 8(2) - 6 = 16 - 6 = 10.
Therefore, the measures of angle B and angle Q are both 10.