The intersection of lines l and m forms the 4 angles `/_A, /_B, /_C, and /_D`. The measure of `/_B` is `3 1/2` times the measure of `/_A`. Which of the following values is closest to the measure of `/_A`?

Options

A. `20^(@)`
B. `26^(@)`
C. `35^(@)`
D. `40^(@)`

Answer

To solve the problem, we need to find the measure of angle A given that the measure of angle B is \(3 \frac{1}{2}\) times the measure of angle A.

### Step-by-Step Solution:

1. **Define the Angles:**
Let the measure of angle A be \(x\). According to the problem, the measure of angle B is \(3 \frac{1}{2}\) times the measure of angle A. We can express this as:
\[ \text{Angle B} = 3.5x = \frac{7}{2}x \]

2. **Use the Straight Line Property:**
Since angles A and B are on a straight line, they must sum up to \(180^\circ\):
\[ x + \frac{7}{2}x = 180^\circ \]

3. **Combine Like Terms:**
To combine the terms on the left side, we can rewrite \(x\) as \(\frac{2}{2}x\):
\[ \frac{2}{2}x + \frac{7}{2}x = \frac{9}{2}x \]
Therefore, we have:
\[ \frac{9}{2}x = 180^\circ \]

4. **Solve for x:**
To isolate \(x\), multiply both sides by \(\frac{2}{9}\):
\[ x = 180^\circ \times \frac{2}{9} \]
\[ x = 40^\circ \]

5. **Conclusion:**
The measure of angle A is \(40^\circ\).

### Final Answer:
The value closest to the measure of angle A is \(40^\circ\).

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