Two angles lie along a straight line. If m∠A is four times the sum of m∠B plus 17.5°, how many degrees is m∠B?
A) 10°
B) 15°
C) 20°
D) 25°
Two angles lie along a straight line. If m∠A is four times the sum of m∠B plus 17.5°, how many degrees is m∠B?
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To solve the problem, we know that two angles along a straight line sum to 180°. We can express this relationship using the angles A and B.
1. According to the problem, we have the following equation:
[
m∠A + m∠B = 180°
]
2. It is also given that:
[
m∠A = 4(m∠B + 17.5°)
]
3. Now, substitute ( m∠A ) in the first equation:
[
4(m∠B + 17.5°) + m∠B = 180°
]
4. Distributing the 4:
[
4m∠B + 70° + m∠B = 180°
]
5. Combine like terms:
[
5m∠B + 70° = 180°
]
6. Subtract 70° from both sides:
[
5m∠B = 110°
]
7. Now divide by 5 to find ( m∠B ):
[
m∠B = 22°
]
However, it seems 22° is not one of the multiple-choice options provided (10°, 15°, 20°, 25°). Let’s check the logic again.