4. Two adjacent angles, ∠21 and ∠22, form a resulting angle with measure 161°. If m∠1 = (4n)° and m∠2 = (4n+1)°, what are the two unknown angle measures?
Let's use the given information to set up an equation. We know that the sum of the two adjacent angles (∠21 and ∠22) is equal to 161°. Using the information given about the angle measures, we can set up the equation:
∠21 + ∠22 = 161°
Since ∠21 has a measure of (4n)° and ∠22 has a measure of (4n+1)°, we can substitute these values into the equation:
(4n)° + (4n+1)° = 161°
Combining like terms:
8n + 1 = 161
Subtracting 1 from both sides:
8n = 160
Dividing both sides by 8:
n = 20
Now that we know the value of n, we can substitute it back into the expressions for the angle measures:
∠21 = (4n)° = (4 * 20)° = 80°
∠22 = (4n+1)° = (4 * 20 + 1)° = 81°
Therefore, the two unknown angle measures are 80° and 81°.
wrong
Apologies for the mistake. Let's correct the solution.
The given information states that ∠21 and ∠22 are adjacent angles that form a resulting angle of 161°. We are also given that ∠21 has a measure of (4n)° and ∠22 has a measure of (4n+1)°.
We can set up the equation using the given information:
∠21 + ∠22 = 161°
Substituting the expressions for ∠21 and ∠22:
(4n)° + (4n+1)° = 161°
Combining like terms:
8n + 1 = 161
Subtracting 1 from both sides:
8n = 160
Dividing both sides by 8:
n = 20
Now that we know the value of n, we can substitute it back into the expressions for the angle measures:
∠21 = (4n)° = (4 * 20)° = 80°
∠22 = (4n+1)° = (4 * 20 + 1)° = 81°
Therefore, the two unknown angle measures are 80° and 81°.
wrong like the song
Apologies for the incorrect response. Let's try to solve the problem again.
We are given that ∠21 has a measure of (4n)° and ∠22 has a measure of (4n+1)°. The sum of these two angles is equal to 161°.
So, we can set up the equation:
(4n)° + (4n+1)° = 161°
Combining like terms:
8n + 1 = 161
Subtracting 1 from both sides:
8n = 160
Dividing both sides by 8:
n = 20
Now that we know the value of n, we can substitute it back into the expressions for the angle measures:
∠21 = (4n)° = (4 * 20)° = 80°
∠22 = (4n+1)° = (4 * 20 + 1)° = 81°
Therefore, the two unknown angle measures are 80° and 81°.