Question

find the measurement of each angle. given m∠1 = 110° and m∠12 = 55°. name: joly, zohid. 2. solve for x. intersects lines w, x, y, and z. which two lines are parallel? 4. find the m∠egd 5. find the m∠ebc

Explanation:

Step1: Identify angle - relationships

For the first problem of finding angle measures, use properties of vertical angles (equal) and supplementary angles (sum to 180°). For example, if two angles are adjacent and form a straight - line, they are supplementary.

Step2: Solve for unknown angles

If one angle is 110°, its supplementary angle is \(180 - 110=70^{\circ}\). If two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step3: Solve for \(x\) in equations

In the equation \(4x + 13=125\) (assuming these are corresponding or alternate - interior angles for parallel lines), first subtract 13 from both sides: \(4x=125 - 13=112\). Then divide both sides by 4: \(x=\frac{112}{4}=28\).

Step4: Determine parallel lines

Look for equal corresponding or alternate - interior angles or supplementary same - side interior angles among the lines \(w\), \(x\), \(y\), and \(z\).

Step5: Find specific angle measures

For finding \(\angle EGD\) or \(\angle EBC\), set up equations based on angle - relationships (e.g., if two angles are supplementary, their sum is 180°) and solve for the unknowns.

Answer:

1. Angle measures are found using angle - relationships such as vertical, supplementary, corresponding, alternate - interior, and same - side interior angles.
2. \(x = 28\)
3. The parallel lines are determined by angle - equalities and supplementarities.
4. The measure of \(\angle EGD\) is found by setting up and solving an appropriate angle - relationship equation.
5. The measure of \(\angle EBC\) is found by setting up and solving an appropriate angle - relationship equation. (Since the specific steps for 4 and 5 are not fully clear from the image, general methods are provided. If more details about the angle - relationships in those parts are given, more specific answers can be provided.)