Given △ABC≅△PQR,∡B=3v+4, and ∡Q∡=8v−6, find ∡B and ∡Q.
(1 point)
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But, since △ABC≅△PQR, ∡B≅∡Q, so
3v+4 = 8v-6
v = 2
and m∡B = m∡Q = 10°
Apologies for the incorrect initial response.
You are correct. Since △ABC≅△PQR, ∠B≅∠Q.
Setting up the equation 3v+4 = 8v-6 and solving for v:
3v+4 = 8v-6
10 = 5v
v = 2
Therefore, ∠B = ∠Q = 3(2) + 4 = 10°.
To find the angles ∡B and ∡Q, we need to use the fact that △ABC is congruent to △PQR.
Since △ABC is congruent to △PQR, it means that the corresponding angles are equal. Therefore, ∡B = ∡Q.
If we substitute ∡B = 3v + 4 and ∡Q = 8v - 6, we can solve for v.
3v + 4 = 8v - 6
First, let's isolate the variable on one side:
4 + 6 = 8v - 3v
10 = 5v
Now, divide both sides of the equation by 5:
10/5 = 5v/5 => 2 = v
Now that we know the value of v, we can substitute it back into either ∡B or ∡Q to find the angle.
Let's substitute it into ∡B = 3v + 4:
∡B = 3(2) + 4
∡B = 6 + 4
∡B = 10
Therefore, ∡B = 10.
Since ∡B = ∡Q, we can conclude that ∡Q = 10.
To find ∠B, we can set up an equation using the fact that corresponding angles of congruent triangles are congruent:
∠B = ∠P (corresponding angles of congruent triangles are congruent)
Since ∠P∠ is not given in the information given, we cannot determine the exact value of ∠B.
To find ∠Q, we can set up an equation using the fact that corresponding angles of congruent triangles are congruent:
∠Q = ∠C (corresponding angles of congruent triangles are congruent)
Since ∠C∠ is not given in the information given, we cannot determine the exact value of ∠Q.