Answer:
1. They are supplementary | 2. <ZYW = 140
Explanation:
1. XW is a line, and if you cover the ray YU you can see that the ray YZ is in common for both angles. This means that the two angles will necessarily add up to 180 degrees, also known as supplementary angles.
2. This is easier to understand using the diagram. Bisection means that the ray is splitting the angle in 2 equal or congruent parts. This means that the two angles that the ray YU creates in between <XYZ are equal.
The expressions for <XYU and <UYZ are 2x + 15 and 4x + 10. These can be set equal to each other.
2x + 15 = 4x + 10. subtract 10 on both sides.
2x + 5 = 4x. subtract 2x from both sides.
5 = 2x. Divide 2 from both sides.
x = 2.5. Now substitute x in both expressions and add them together to get the m<XYZ.
2(2.5) + 15 + 4(2.5) + 10 = 40. Using the information from question 1, we know that <XYZ + <ZYW = 180. 180 - 40 = 140. <ZYW = 140.
The diagram seems to not be to scale, which is fine because that happens sometimes in geometry.