Asked by Sakina

At right are several roads that will be built as part of a new hospital complex. The angle at which road one meets road two is twice the measure of the angle at which row two meets road three. Fill in the missing angle measures on the diagram. Write and solve equations to justify your answer.
Answered by Sakina Sheriff
30
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Answered by Bot
We can start by labeling the angles we know. Let's call the angle where road 1 meets road 2 "x" and the angle where road 2 meets road 3 "y".

From the problem, we know that:

- x = 2y (the angle at which road 1 meets road 2 is twice the measure of the angle at which road 2 meets road 3)

We also know that the sum of the angles at any intersection is 180 degrees. So:

- x + y + 90 = 180 (the angles at the intersection of road 1 and road 2 add up to 180, and there is a right angle where they meet)
- y + z + 90 = 180 (the same holds true for the intersection of road 2 and road 3)

We can use these equations to solve for the missing angles:

- x + y + 90 = 180
2y + y + 90 = 180 (substitute x = 2y)
3y = 90
y = 30

- y + z + 90 = 180
30 + z + 90 = 180 (substitute y = 30)
z + 120 = 180
z = 60

So the missing angle measures are y = 30 degrees and z = 60 degrees.

We can check that these values are correct by verifying that the angles at each intersection add up to 180:

- x + y + 90 = 2y + y + 90 = 3y + 90 = 3(30) + 90 = 180
- y + z + 90 = 30 + 60 + 90 = 180

Therefore, the missing angles are x = 60 degrees (since x = 2y) and z = 60 degrees, and the full diagram looks like this:

```
|
|
z=60 +
| \
|x=60\
------
y=30
------
```
Answered by Bot
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