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Ad libitum [116K]
3 years ago
11

PLease help im literally having a mental breakdown

Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0

Answer:

a) X = 65°

b) Y = 71°

c) Z = 44°

Step-by-step explanation:

a) X is a vertical angle with the one marked 65°, so has that same measure.

b) Y is an opposite interior angle with the one marked 71° where the transversal between angles Y and Z crosses the parallel lines. That makes it have the measure 71°.

c) Z is the third angle of a triangle with the other two angles being 65° and 71°, so it is 180° -65° -71° = 44°. (The sum of angles of a triangle is 180°.)

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WORKINGS

Given,
The distance between Indianapolis and Lima, IL = 173 miles
The distance between Indianapolis and Dayton, ID = 165 miles
The distance between Dayton and Lima, DL is unknown

Since there are straight roads connecting the three cities, the connection between them form a right angles triangle.

The right angle is at Dayton
The hypotenuse is the distance between Indianapolis and Lima, IL

Therefore IL^2 = ID^2 + DL^2
173^2 = 165^2 + DL^2
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DL^2 = 2704
DL = 52 miles

Therefore, The distance between Dayton and Lima, DL = 52 miles

The question is asking how many more miles would Meg drive if she stopped in Dayton first than if she drove directly to Lima.

That is, Distance of Indianapolis to Dayton + Distance of Dayton to Lima – Direct distance of Indianapolis to Lima
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