Alright, let's solve this step by step.
1. Determine the measure of angle 3:
- We are given the expression for the measure of angle 3 as \((2x + 6)^{\circ}\).
- We know that \(x = 7\), so we substitute \(x\) with 7 in the expression for angle 3.
[tex]\[
\text{Measure of angle 3} = 2(7) + 6 = 14 + 6 = 20^{\circ}
\][/tex]
2. List the given measures of other angles:
- Measure of angle 6 is \(20^{\circ}\).
- Measure of angle 5 is \(70^{\circ}\).
- Measure of angle 2 is \(80^{\circ}\).
3. Compare the measure of angle 3 with the given angles:
- The measure of angle 3 is \(20^{\circ}\).
- We compare this value with the given angles' measures:
- Measure of angle 6 is \(20^{\circ}\) \( \Rightarrow \) This statement is true.
- Measure of angle 5 is \(70^{\circ}\) \( \Rightarrow \) This statement is false.
- Measure of angle 2 is \(80^{\circ}\) \( \Rightarrow \) This statement is false.
4. Identify the true statements:
- The only true statement is: The measure of angle 6 is \(20^{\circ}\).
Therefore, the correct answer is:
- The measure of angle 6 is \(20^{\circ}\).
The statements "The measure of angle 5 is [tex]\(70^{\circ}\)[/tex]" and "The measure of angle 2 is [tex]\(80^{\circ}\)[/tex]" are not true.
