Examine the diagram to the right then use the information provided in the diagram to find the measures of angles x , y, z. for each angle, name the angle relationship that justify your conclusion.

Step-by-step explanation:

The letters are virtually impossible to read. I'll do my best, but recognize it is why you are not getting answers. I take y to be next to the 100 degree angle and part of the triangle.

I take x to be to the left of y. It is equal to the 28o angle because of the tranversal properties.

Finally z is the exterior angle of the triangle and as such has properties of z = y + 28 where y and 28 are remote interior angles to the triangle.

so x = 28 because of the transversal cutting the two parallel lines. They are equal by remote exterior angles of parallel lines.

y = 180 - 100 - 28 = 52

Finally z = 52 + 28 = 80 degrees because x and y add to 80 degrees.

If the assumptions are incorrect, could I trouble you to repost the diagram or correct the errors I  have made.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.