Question: Given that segment $ab$ is parallel to segment $dc$ that the measure of angle one equals 112, the measure of angle two equals 4x and the measure of angle three equals 3x + 12, find the measure of angle two
1. **State the problem:** We are given that segment $ab$ is parallel to segment $dc$, and the measures of three angles: angle one is $112^\circ$, angle two is $4x$, and angle three is $3x + 12$. We need to find the measure of angle two.
2. **Identify relationships:** Since $ab \parallel dc$, angles one, two, and three are related by the properties of parallel lines and transversals. Typically, angles on a straight line sum to $180^\circ$.
3. **Set up the equation:** Angles two and three are adjacent and likely supplementary (sum to $180^\circ$), so:
$$4x + (3x + 12) = 180$$
4. **Simplify the equation:**
$$4x + 3x + 12 = 180$$
$$7x + 12 = 180$$
5. **Isolate $x$:**
$$7x = 180 - 12$$
$$7x = 168$$
6. **Solve for $x$:**
$$x = \frac{168}{7}$$
$$x = 24$$
7. **Find angle two:**
$$\text{angle two} = 4x = 4 \times 24 = 96^\circ$$
**Final answer:** The measure of angle two is $96^\circ$.