Question: User: \(\angle 1\) and \(\angle 2\) are complementary angles. If \(m\angle 1=(8x-17)\) \(^\circ\) and \(m\angle 2=(6x+9)\) \(^\circ\), then find the measure of \(\angle 1\).
1. **State the problem:** We are given two complementary angles \(\angle 1\) and \(\angle 2\) with measures \(m\angle 1 = (8x - 17)^\circ\) and \(m\angle 2 = (6x + 9)^\circ\). We need to find the measure of \(\angle 1\).
2. **Recall the definition of complementary angles:** Two angles are complementary if the sum of their measures is \(90^\circ\). So,
$$m\angle 1 + m\angle 2 = 90^\circ$$
3. **Set up the equation:** Substitute the given expressions:
$$(8x - 17) + (6x + 9) = 90$$
4. **Simplify the equation:**
$$8x - 17 + 6x + 9 = 90$$
$$14x - 8 = 90$$
5. **Isolate \(x\):**
$$14x - 8 = 90$$
$$14x = 90 + 8$$
$$14x = 98$$
$$x = \frac{98}{14}$$
$$x = 7$$
6. **Find \(m\angle 1\):** Substitute \(x=7\) into \(m\angle 1 = 8x - 17\):
$$m\angle 1 = 8(7) - 17 = 56 - 17 = 39^\circ$$
7. **Final answer:** The measure of \(\angle 1\) is \(39^\circ\).