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tatiyna
3 years ago
9

(02.07)Which relationship is always true for the angles x, y, and z of triangle ABC? A triangle is shown with a leg extending pa

st the top vertex. The vertices are labeled ABC. Angle y is located inside the triangle at vertex B. Angle z is located inside the triangle at vertex C. Angle x is located outside the triangle between side AC and the extended leg.

Mathematics
2 answers:
Lerok [7]3 years ago
5 0
Did you notice that the vertices of the triangle A, B, C go in clockwise direction?

zysi [14]3 years ago
3 0
Check out the attached image. I drew what I think your book is showing. The figure on the left is triangle ABC without any extended segments. The figure on the right has segment AB extended shown in red. This forms the exterior angle x

The rule that connects x, y and z together is the remote interior angle theorem. It says that adding two interior angles is going to be equal to the exterior angle that is not touching either interior angle. The "remote" part means "far away" so just think of the two angles that are furthest way or not touching the exterior angle in question. 

In terms of algebra, the rule is
x+y = z

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3 years ago
Howard is standing 87 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the wat
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He is 174 yards from the top.

Since we have a 60° angle and a right angle, this is a 30-60-90 triangle.  In these triangles, we can label the sides as t, t√3 and 2t, with t being the side opposite the 30° angle (the smallest side); t√3 being the side opposite the 60° angle (the middle side); and 2t being the hypotenuse (the longest side).

Our 87 yard side is across from the 30° angle, so it is t.

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