Two railroad tracks cross each other as shown If the measure

Two railroad tracks cross each other, as shown. If the measure of angle 1 is 3 times the measure of angle 2, what are the measures of angles 1, 2, 3, and 4? Explain and show your work. At right are several roads that will be built as part of a new hospital complex. The angle at which Road 1 meets Road 2 is twice the measure of the angle at which Road 2 meets Road 3. Fill in the missing angle measures on the diagram. Write and solve equations to justify your answers.

Solution

17)

Let angle 1 = a

Let angle 2 = b

Let angle 3 = c

Let angle 4 = d

So

a=3b

Since a+b= 180

4b= 180

b=45

a=135,

Since c and d are opposite angles to a and b respectively,

c=135

d=45

18)

Let angle between road 1 and road 2 =a degree

and angle between road 2 and road 3 = b degree

since angle between road 3 and road 1 = 90 degree,

Therefore a+b= 90 degree

But as it is given, a = 2b

Therefore 3b= 90 degree

b= 30 degree

and a = 60 degree