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