Answer:
A, B: False
C, D, E: True
Step-by-step explanation:
The angle sum theorem and the definition of a linear pair of angles can help you answer these questions.
<h3>A.</h3>
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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<h3>B.</h3>
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.
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<h3>C.</h3>
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."
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<h3>D.</h3>
m = 180° -x; True. This is exactly what we mean when we say angles m and x are a <em>linear pair</em>. 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.
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<h3>E.</h3>
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
