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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?

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°




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What is the capital of Egypt? ( Cairo )

1 Answer

  1. 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.

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