Question: User: . Notice that measurement will 3 plus the measure of angle 4 plus measure of angle 5 has to equal a 180.And so use the expressions to set up an equation with that , and solve the equation for x , then use your answer for x to find the measure of angle three
1. **State the problem:** We are given that the measure of angle 3 plus the measure of angle 4 plus the measure of angle 5 equals 180 degrees. We need to set up an equation using expressions for these angles, solve for $x$, and then find the measure of angle 3.
2. **Set up the equation:** Suppose the measures of angles 3, 4, and 5 are given by expressions involving $x$. Let these be $m_3$, $m_4$, and $m_5$ respectively. The problem states:
$$m_3 + m_4 + m_5 = 180$$
3. **Use the given expressions:** Since the problem does not specify the exact expressions for angles 3, 4, and 5, assume they are provided as:
$$m_3 = 2x + 10$$
$$m_4 = 3x - 5$$
$$m_5 = x + 15$$
(If your expressions differ, replace these accordingly.)
4. **Form the equation:**
$$2x + 10 + 3x - 5 + x + 15 = 180$$
5. **Simplify the equation:**
$$2x + 3x + x + 10 - 5 + 15 = 180$$
$$6x + 20 = 180$$
6. **Solve for $x$:**
Subtract 20 from both sides:
$$6x + \cancel{20} - \cancel{20} = 180 - 20$$
$$6x = 160$$
Divide both sides by 6:
$$\frac{6x}{6} = \frac{160}{6}$$
$$x = \frac{160}{6} = \frac{80}{3} \approx 26.67$$
7. **Find the measure of angle 3:**
Substitute $x = \frac{80}{3}$ into $m_3 = 2x + 10$:
$$m_3 = 2 \times \frac{80}{3} + 10 = \frac{160}{3} + 10 = \frac{160}{3} + \frac{30}{3} = \frac{190}{3} \approx 63.33$$
**Final answer:** The measure of angle 3 is approximately $63.33$ degrees.