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°
(quick question: what would be the symbol for "angle" on here?)
How do I solve this????
STEP-BY-STEP would be amazing! Thank you.
m∠B = m∠Q
3v+4 = 8v-6
v = 2
So, m∠B = m∠Q = 10°
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! 🤡
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.