Question

exterior angles of triangles
the sum of x and y is equal to which angle?
a v
b w
c x
what is the relationship between w and y?
a w < y
b w > y
c w = y
what is the relationship between x and w?
a x < w
b x > w
c x = w
exterior angle theorem
00:03: the exterior angle theorem. what is the exterior angle theorem? it states that the measure of the exterior angle of a triangle is greater than either of the measures of the remote interior angles. so if we look at our diagram here, what that means is by this theorem, the measure of angle w has to be bigger than the measure of angle x, and the measure of angle w has to be bigger than the measure of angle y. so why does this work? well, lets look at it. so what do we know? we know that the three angles of a triangle have to sum up to be 180 degrees. so we know x plus y plus z must equal 180 degrees. what else do we know? we know that these angles w and z right here form a linear pair. so the sum of those two angles, so w plus z, must also equal 180 degrees. so, in both of these equations, we have the variable z, so lets solve for it. so in the first one, z equals 180 degrees minus x plus y, that quantity. and z in the second equation equals 180 degrees minus w. so notice that z in both cases here is the subtraction of that and the subtraction of that, which has to mean that x plus y equals w. so, if x plus y equals w, then w must be larger than both x and y.

Explanation:

First Question:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Identify the angles

In a triangle, if \(x\) and \(y\) are non - adjacent interior angles and \(w\) is the exterior angle, then \(x + y=w\) (by the exterior angle theorem).

Second Question:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the measure of an exterior angle (\(w\)) of a triangle is greater than either of the measures of the remote interior angles (\(x\) and \(y\)). So \(w>y\)

Third Question:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the measure of an exterior angle (\(w\)) of a triangle is greater than either of the measures of the remote interior angles (\(x\) and \(y\)). So \(x < w\)

Answer:

1. B. \(w\)
2. B. \(w>y\)
3. A. \(x < w\)