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39 votes
39 votes
Is each statement true or false?

Explain your answers
A.

m \: = x
B.

z \: = x + y
C.

m \: = y + z
D.

m = 180 - x
E.

x = 180 - (y + z)

(the triangle is on the image)






Is each statement true or false? Explain your answers A. m \: = x B. z \: = x + y-example-1
User Pellizon
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1 Answer

22 votes
22 votes

Answer:

A, B: False

C, D, E: True

Explanation:

The angle sum theorem and the definition of a linear pair of angles can help you answer these questions.

A.

m = x; False. Angles m and x are a linear pair. They are supplementary (total 180°). They are only equal if they are both 90°, which is not indicated in this diagram as being the case.

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B.

z = x+y; False. Angles x, y, and z total 180° according to the angle sum theorem. The equation is only true if z = 90°, which is not indicated in this diagram as being the case.

__

C.

m = y +z; True. This is explained by the equations of D and E, which are also both true. The theorem that expresses this relationship is, "an exterior angle is equal to the sum of the remote interior angles."

__

D.

m = 180° -x; True. This is exactly what we mean when we say angles m and x are a linear pair. Together, they form a straight line. The angles of a linear pair are supplementary, meaning their sum is 180°. Angle m is also called an "external angle" of the triangle.

__

E.

x = 180° -(y +z); True. The angles of a triangle total 180° according to the angle sum theorem. That means the value of any one of them is the difference between 180° and the sum of the other two. This is effectively telling you that angle x is supplementary to the sum of angles y and z.

Above, we noted that angle x is supplementary to angle m. Angles that are supplementary to the same angle have the same measure, so ...

m = 180° -x

180° -x = y +z . . . . . rearrange equation E

m = y +z

User Eaj
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2.7k points