Question: User: \(\angle 1\) and \(\angle 2\) are supplementary angles. If \(m\angle 1=(5x+25)\) \(^\circ\) and \(m\angle 2=(3x-21)\) \(^\circ\) , then find the measure of \(\angle 2\).
1. **State the problem:** We are given two supplementary angles \(\angle 1\) and \(\angle 2\) with measures \(m\angle 1 = 5x + 25\) degrees and \(m\angle 2 = 3x - 21\) degrees. We need to find the measure of \(\angle 2\).
2. **Recall the rule for supplementary angles:** Supplementary angles add up to \(180^\circ\). So,
$$m\angle 1 + m\angle 2 = 180$$
3. **Set up the equation:** Substitute the given expressions:
$$ (5x + 25) + (3x - 21) = 180 $$
4. **Simplify the equation:**
$$ 5x + 25 + 3x - 21 = 180 $$
$$ (5x + 3x) + (25 - 21) = 180 $$
$$ 8x + 4 = 180 $$
5. **Isolate \(x\):**
$$ 8x + 4 = 180 $$
$$ 8x = 180 - 4 $$
$$ 8x = 176 $$
6. **Divide both sides by 8:**
$$ x = \frac{176}{8} $$
$$ x = \cancel{\frac{176}{\cancel{8}}} \cancel{\frac{\cancel{8} \times 22}{8}} = 22 $$
7. **Find \(m\angle 2\):** Substitute \(x=22\) into \(m\angle 2 = 3x - 21\):
$$ m\angle 2 = 3(22) - 21 = 66 - 21 = 45 $$
**Final answer:** \(m\angle 2 = 45^\circ\).