If triangle ZXY is an equilateral triangle and the measure of W equals 34 degrees, what is the measure of the triangle WXZ?
Work: XZ bisects WXZ and ZXY ; since W is 34 degrees, than Y is 34 degrees and since ZXY is equilateral, that also means that Z is 34 degrees.
To find the measure of triangle WXZ, we need to determine the measure of angle X.
Since triangle ZXY is an equilateral triangle, all three angles in the triangle are equal. Therefore, the measure of angle ZXY is also 60 degrees.
We know that angle XZ bisects angle ZXY, which means that it splits the angle into two equal parts. So, angle ZXA is also 30 degrees.
Now, we can use the angles in a triangle property: the sum of angles in a triangle is always 180 degrees. Therefore, we can write the equation as:
Angle Z + Angle X + Angle ZA = 180 degrees.
Substituting the known values, we have:
34 degrees + 30 degrees + Angle WXZ = 180 degrees.
Now, we can solve for Angle WXZ:
Angle WXZ = 180 degrees - (34 degrees + 30 degrees)
= 180 degrees - 64 degrees
= 116 degrees.
So, the measure of triangle WXZ is 116 degrees.
Can't quite fathom your terminology.
How do you take the measure of a triangle? I'll assume that WXZ is an angle, not a triangle.
If XZ is a side of the triangle ZXY, how can it bisect ZXY?
I'll assume your logic is sound, even if your exposition is not.