Given ∆ABC≅∆PQR,m (angle)B=3v+4,and m(angle)Q=8v-6,find m(angle)B and m(angle)Q

If the triangles are congruent, the corresponding angles are equal. So,

m∠B = m∠Q
3v+4 = 8v-6
v = 2

So, m∠B = m∠Q = 10°

thanks

thx

Thanks

thx

Well, isn't this a triangle-tastic challenge! Let's get to solving it, step-by-step, just as you requested! 🎉

Step 1: Given that ∆ABC ≅ ∆PQR, we know that the corresponding angles of these triangles will be congruent.

Step 2: To find the measure of angle B and angle Q, we'll need to use the given expressions. So, m(angle)B = 3v + 4, and m(angle)Q = 8v - 6.

Step 3: Since the two triangles are congruent, the measure of angle B in ∆ABC will be equal to the measure of angle Q in ∆PQR. So, we can set up an equation:

3v + 4 = 8v - 6

Step 4: Let's solve this equation and find the value of v:

First, let's gather the v terms on one side:

3v - 8v = -6 - 4
-5v = -10

Then, divide both sides of the equation by -5:

v = -10 / -5
v = 2

Step 5: Now that we know the value of v, let's substitute it back into the expressions for angle B and angle Q:

m(angle)B = 3(2) + 4
m(angle)B = 6 + 4
m(angle)B = 10

m(angle)Q = 8(2) - 6
m(angle)Q = 16 - 6
m(angle)Q = 10

So, we have discovered that m(angle)B = 10 and m(angle)Q = 10! 🎉

Hope this clownish explanation brought a smile to your face while solving your geometry problem! Have a clown-tastic day! 🤡

To solve this problem, we can start by setting up an equation using the given information.

1. Write the equation for the congruence of the triangles ∆ABC and ∆PQR: ∆ABC ≅ ∆PQR.

2. List the corresponding angles: angle B in ∆ABC corresponds to angle Q in ∆PQR.

3. Set up an equation using the given angle measures:
m(angle B) = 3v + 4
m(angle Q) = 8v - 6

4. Since the two triangles are congruent, their corresponding angles are equal. Therefore, we can set up an equation by equating the given angle measures:
3v + 4 = 8v - 6

Now, let's solve for v and then find the values of m(angle B) and m(angle Q) using the obtained value of v.

5. Rearrange the equation to isolate the variable v on one side:
3v - 8v = -6 - 4
-5v = -10

6. Divide both sides by -5 to solve for v:
v = (-10) / (-5)
v = 2

7. Substitute the value of v back into the equation to find the angle measures:
m(angle B) = 3v + 4
m(angle B) = 3(2) + 4
m(angle B) = 6 + 4
m(angle B) = 10

m(angle Q) = 8v - 6
m(angle Q) = 8(2) - 6
m(angle Q) = 16 - 6
m(angle Q) = 10

So, the values of m(angle B) and m(angle Q) are both 10.

Note: The symbol for "angle" is usually represented by a curved line or by writing the letters that constitute the angle, such as ∠B or ∠Q.