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?

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.