To determine the largest angle among the three given angles, let's carefully evaluate each one.
We have the following angles:
1. [tex]\( 20^\circ \)[/tex]
2. [tex]\( 20^\circ \)[/tex]
3. [tex]\( 2x + 10^\circ \)[/tex]
Since the first two angles are fixed at [tex]\( 20^\circ \)[/tex], our primary comparison involves the angle expressed as [tex]\( 2x + 10^\circ \)[/tex].
### Step-by-Step Solution:
1. Identify the Angles:
- The first angle: [tex]\( 20^\circ \)[/tex]
- The second angle: [tex]\( 20^\circ \)[/tex]
- The third angle: [tex]\( 2x + 10^\circ \)[/tex]
2. Comparison: To find the largest angle, compare [tex]\( 2x + 10^\circ \)[/tex] with [tex]\( 20^\circ \)[/tex].
3. Determine the Condition:
- For [tex]\( 2x + 10^\circ \)[/tex] to be the largest angle, it must be greater than [tex]\( 20^\circ \)[/tex].
- Thus, we need to solve the inequality:
[tex]\[
2x + 10 > 20
\][/tex]
4. Solve the Inequality:
[tex]\[
2x + 10 > 20
\][/tex]
Subtract 10 from both sides:
[tex]\[
2x > 10
\][/tex]
Divide both sides by 2:
[tex]\[
x > 5
\][/tex]
### Conclusion:
For [tex]\( x > 5 \)[/tex], the angle [tex]\( 2x + 10^\circ \)[/tex] becomes greater than [tex]\( 20^\circ \)[/tex]. When [tex]\( x \)[/tex] is any value greater than 5, [tex]\( 2x + 10^\circ \)[/tex] will surpass the other two angles, making it the largest one.
#### Summary:
- If [tex]\( x \leq 5 \)[/tex], the largest angle is [tex]\( 20^\circ \)[/tex].
- If [tex]\( x > 5 \)[/tex], the largest angle is [tex]\( 2x + 10^\circ \)[/tex].
Thus, the largest angle depends on the value of [tex]\( x \)[/tex]. For [tex]\( x > 5 \)[/tex], [tex]\( 2x + 10^\circ \)[/tex] will be larger than the two fixed angles of [tex]\( 20^\circ \)[/tex].
