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°.
The measure of angle 2 is 80°.
Angles 2 and 5 are complementary.
Angles 5 and 6 are supplementary.
Angles 1 and 4 are supplementary.
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°.
The measure of angle 2 is 80°.
Angles 2 and 5 are complementary.
Angles 5 and 6 are supplementary.
Angles 1 and 4 are supplementary.
Answers
GPT-4o mini
To determine which statements are true, we first need to find the measure of angle 3 using the provided formula and the value of \( x \).
Given:
\[
\text{Angle 3} = (2x + 6)^\circ
\]
and
\[
x = 7
\]
Calculating the measure of angle 3:
\[
\text{Angle 3} = (2 \cdot 7 + 6)^\circ
\]
\[
= (14 + 6)^\circ
\]
\[
= 20^\circ
\]
Now that we know angle 3 measures 20°, let’s summarize what we know from the diagram:
- Angle 1 measures 90°.
- Angle 6 measures 20° (given).
- Angle 5 measures 70° (given).
- Angle 2 measures 80° (given).
Now we can analyze the relationships among the angles to verify the statements:
1. **Angles 2 (80°) and 5 (70°) are complementary.**
- Complementary angles sum to 90°:
\[
80° + 70° = 150°
\]
- This statement is **false**.
2. **Angles 5 (70°) and 6 (20°) are supplementary.**
- Supplementary angles sum to 180°:
\[
70° + 20° = 90°
\]
- This statement is **false**.
3. **Angles 1 (90°) and 4 (not given, but we can deduce it) are supplementary.**
- Since angles 1 and 2 are vertical angles, angle 2 is 80°.
- Since angle 1 is 90°, angle 4 (which is vertically opposite) would also be 90°.
- Thus, angle 1 (90°) and angle 4 (90°) add up to 180°, making this statement **true**.
In conclusion, after analyzing the statements related to the measures of the angles that are given and calculated, only **"Angles 1 and 4 are supplementary"** is **true**. All the other statements are **false**.
Given:
\[
\text{Angle 3} = (2x + 6)^\circ
\]
and
\[
x = 7
\]
Calculating the measure of angle 3:
\[
\text{Angle 3} = (2 \cdot 7 + 6)^\circ
\]
\[
= (14 + 6)^\circ
\]
\[
= 20^\circ
\]
Now that we know angle 3 measures 20°, let’s summarize what we know from the diagram:
- Angle 1 measures 90°.
- Angle 6 measures 20° (given).
- Angle 5 measures 70° (given).
- Angle 2 measures 80° (given).
Now we can analyze the relationships among the angles to verify the statements:
1. **Angles 2 (80°) and 5 (70°) are complementary.**
- Complementary angles sum to 90°:
\[
80° + 70° = 150°
\]
- This statement is **false**.
2. **Angles 5 (70°) and 6 (20°) are supplementary.**
- Supplementary angles sum to 180°:
\[
70° + 20° = 90°
\]
- This statement is **false**.
3. **Angles 1 (90°) and 4 (not given, but we can deduce it) are supplementary.**
- Since angles 1 and 2 are vertical angles, angle 2 is 80°.
- Since angle 1 is 90°, angle 4 (which is vertically opposite) would also be 90°.
- Thus, angle 1 (90°) and angle 4 (90°) add up to 180°, making this statement **true**.
In conclusion, after analyzing the statements related to the measures of the angles that are given and calculated, only **"Angles 1 and 4 are supplementary"** is **true**. All the other statements are **false**.