Name two pairs of adjacent angels and two pairs of vertical angels in figure

As in this case where the adjacent angles are formed by two lines intersecting we will get two pairs of adjacent angles (G + F and H + E) that are both supplementary. Two angles that are opposite each other as D and B in the figure above are called vertical angles. Vertical angles are always congruent

Step-by-step explanation:

Complete question :

The distance from town X to town Y is 200 km. The distance from town X to town Z is 135 km. Looking from town Y, town X and town Z are separated by an angle of 42°. Sketch possible diagrams for this situation. Calculate the possible distances from town Y to town Z.

166 km

Step-by-step explanation:

Given that :

X to Y = 200km

X to Z = 135 km

X and Z are separated by 42°

Using Sine rule :

x

z / sinZ = y / sinY

200/ sinZ = 135/sin42

SinZ = (200 * sin42) / 135

SinZ = 0.9913046

Sin^-1 (0.9913)

Z = 82.438

Z = 82.44

Hence,

X = 180 - (Z + Y) (angles in a triangle)

X = 180 - (82.44 + 42)

X = 55.56°

To obtain x:

x / sin X = y / sin Y

x / sin 55.56 = 135 / sin 42

x * sin 42 = sin 55.56 * 135

x = (55.56 * 135) / sin42

x = 111.33704 / 0.6691306

x = 166.39059

Hence, possible Distance from town Y to town Z= 166 km