Question

Given ABC PQR, m B

= 3v + 4, and m Q = 8v – 6,
find m B and m Q.
(1 point)
22
11
10
25

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find m B and m Q, we need to set up an equation using the angle sum property in a triangle.

In triangle ABC, the sum of the three angles is always 180 degrees. Therefore, we can write the equation as:

m B + m C + m A = 180
= 3v + 4 + m C + m A = 180

Similarly, in triangle PQR, the sum of the three angles is also 180 degrees. Therefore, we can write the equation as:

m Q + m R + m P = 180
= 8v - 6 + m R + m P =180

We know that m B = 3v + 4 and m Q = 8v - 6. We can substitute these values into the equations above:

3v + 4 + m C + m A = 180
8v - 6 + m R + m P = 180

Since m C + m A = 180 -m B, and m R + m P = 180 - m Q, we can substitute these values:

3v + 4 + 180 - m B = 180
8v - 6 + 180 - m Q = 180

Now, we can solve for m B and m Q:

3v + 4 + 180 - (3v + 4) = 180
3v + 4 + 180 - 3v - 4 = 180
180 = 180

Therefore, m B = 3v + 4

And,

8v - 6 + 180 - (8v - 6) = 180
8v - 6 + 180 - 8v + 6 = 180
180 = 180

Therefore, m Q = 8v - 6

So, the values of m B and m Q are 3v + 4 and 8v - 6 respectively.

Answer 2

since the two triangles are either similar or congruent (user did not say), we know that angle B≅Q

so, that means that
3v+4 = 8v-6
v = 2
so B = Q = 14°

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, you are correct. Since angle B ≅ angle Q, we can set them equal to each other:

3v + 4 = 8v - 6
4 + 6 = 8v - 3v
10 = 5v
v = 2

Now we substitute v back into the expression for angle B or Q:

Angle B = 3v + 4
Angle B = 3(2) + 4
Angle B = 6 + 4
Angle B = 10

Therefore, angle B = 10°

Similarly,

Angle Q = 8v - 6
Angle Q = 8(2) - 6
Angle Q = 16 - 6
Angle Q = 10

Therefore, angle Q = 10°

So, the measures of angles B and Q are both 10 degrees. Thank you for pointing out the correct approach.