Given AABC = APQR, <B = 3v + 4, and <Q< = 8v - 6, find <B and <Q.
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Given that AABC is congruent to APQR, we know that the corresponding angles are equal. Therefore, <B = <Q.
We have <B = 3v + 4 and <Q = 8v - 6.
To find the value of v, let's equate <B and <Q.
3v + 4 = 8v - 6
Subtracting 3v from both sides, we get:
4 = 5v - 6
Adding 6 to both sides, we get:
10 = 5v
Dividing by 5, we get:
v = 2
Now that we have the value of v, we can substitute it back into either <B or <Q to find the angle measure.
Using <B = 3v + 4:
<B = 3(2) + 4
<B = 6 + 4
<B = 10
Therefore, <B = 10 degrees.
Since <B = <Q, we can conclude that <Q is also equal to 10 degrees.
In conclusion, <B = 10 and <Q = 10.