Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, how many degrees is m∠B?
A) 27.6°
B) 32.4°
C) 15.6°
D) 36.6°
What is the measure of angle B if angle A is five times the sum of angle B plus 7.2 degrees?
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Let’s solve for the measure of angle B (m∠B) step by step.
1. Since angles A and B are along a straight line, they add up to 180 degrees:
[
m∠A + m∠B = 180°
]
2. According to the problem, m∠A is five times the sum of m∠B plus 7.2°. We can express that mathematically:
[
m∠A = 5(m∠B + 7.2°)
]
3. Now we can substitute the expression for m∠A from the second equation into the first:
[
5(m∠B + 7.2°) + m∠B = 180°
]
4. Let’s simplify this equation:
[
5m∠B + 36 + m∠B = 180°
]
[
6m∠B + 36 = 180°
]
5. Now, subtract 36 from both sides:
[
6m∠B = 144°
]
6. Finally, divide by 6 to solve for m∠B:
[
m∠B = 24°
]
Now we can check the multiple-choice options provided. However, it seems none exactly equals 24°. Please