Question

If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true? Check all that apply.

3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1 (90 degrees), 2, 3, 4, 5, 6.
The measure of angle 6 is 20°.
The measure of angle 5 is 70°.
A. The measure of angle 2 is 80°.
B. Angles 2 and 5 are complementary.
C. Angles 5 and 6 are supplementary.
D. Angles 1 and 4 are supplementary.

Answer 1

To find out which statements are true, we first need to calculate the measure of angle 3 using the given value of \( x = 7 \):

\[
\text{Measure of angle 3} = 2x + 6 = 2(7) + 6 = 14 + 6 = 20°
\]

Once we have the measure of angle 3, we can analyze the other angles based on the relationships between them:

1. **Angle 1:** \( 90° \) (as given).
2. **Angle 6:** \( 20° \) (as given).
3. **Angle 5:** \( 70° \) (as given).

### Determine the Measures of Angles 2 and 4:
Since angles around a point add up to \( 360° \), we can find the remaining angles:

- **Measure of Angle 2:**
Angles 1 (90°), 2, and 3 (20°) are appropriately positioned around the intersecting lines. Hence,
\[
90° + \text{Measure of Angle 2} + 20° + \text{Measure of Angle 4} = 180°
\]
Since angle 1 and angle 4 are vertical angles, they are also equal:
\[
\text{Measure of angle 4} = 90°
\]
Therefore,
\[
90° + \text{Measure of Angle 2} + 20° + 90° = 180° \implies \text{Measure of Angle 2} = 180° - 200° = -20°
\]

However clearly angle 2 should then be computed as follows from supplementary angles relation
- **Angle 2 & 3 (20°):**
\[
180° - 20° = 160° \text{(for angle 2)}
\]

- **Measure of Angle 4:** \(90°\) (by vertical angles).

### Now we can check the statements:

**A. The measure of angle 2 is 80°.**
- False. The measure of angle 2 is \(160°\).

**B. Angles 2 and 5 are complementary.**
- False. The measures of angles 2 (160°) and 5 (70°) add up to 230°, not 90°.

**C. Angles 5 and 6 are supplementary.**
- True. The measures of angles 5 (70°) and 6 (20°) add up to 90°, they are not supplementary.

**D. Angles 1 and 4 are supplementary.**
- False. Angle 1 is 90°, and angle 4 is also 90°, so they are equal, not supplementary.

### Conclusion:
Given our findings, the only true statement concerning the angles in this scenario is:

- **None of the statements A, B, C, or D is true based on the data provided and checked**.