Question

If ∠ROQ and ∠ROS are complementary angles, then what is the value of x and m∠ROS?
A.
x = 31; m∠ROS = 62°
B.
x = 60; m∠ROS = 28°
C.
x = 28; m∠ROS = 60°
D.
x = 62; m∠ROS = 31°

Answer 1

To determine the correct values for \( x \) and \( m∠ROS \), we need to use the fact that complementary angles sum up to 90 degrees. If we assume:

- \( m∠ROQ = x \)
- \( m∠ROS = 90 - x \)

We use the given choices to find which values make the pairs of angles complementary. Here are the possible pairs from the options:

1. **Option A**:
- \( x = 31 \)
- \( m∠ROS = 62 \)
- Check: \( 31 + 62 = 93 \) (Not complementary)

2. **Option B**:
- \( x = 60 \)
- \( m∠ROS = 28 \)
- Check: \( 60 + 28 = 88 \) (Not complementary)

3. **Option C**:
- \( x = 28 \)
- \( m∠ROS = 60 \)
- Check: \( 28 + 60 = 88 \) (Not complementary)

4. **Option D**:
- \( x = 62 \)
- \( m∠ROS = 31 \)
- Check: \( 62 + 31 = 93 \) (Not complementary)

None of the provided options produce angles that are complementary (adding to 90°). Therefore, it seems you may want to recheck the values or the question itself, as the information provided does not yield a complementary pair of angles from the given answers.

Let me know if you have additional details or corrections!