Final Answer
The measures of angles in triangle XYZ for the given scenarios are:
A) ∠ZXY = 45°, ∠WXZ = 135°, ∠WXY = 180°
B) ∠ZXY = 45°, ∠WXZ = 45°, ∠WXY = 90°
C) ∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 135°
D) ∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 180°
Step-by-step explanation
In triangle XYZ, we are given the measures of angles ∠ZXY, ∠WXZ, and ∠WXY. To find the measures of the remaining angles, we can use the fact that the sum of the interior angles of a triangle is 180 degrees.
For scenario A, we have:
∠ZXY = 45°, ∠WXZ = 135°, ∠WXY = 180°
We can see that ∠WXY is the only angle that is not given, so we can use the fact that the sum of the interior angles of a triangle is 180 degrees to find its measure.
∠WXY + ∠ZXY + ∠WXZ = 180°
Simplifying, we get:
∠WXY = 180° - ∠ZXY - ∠WXZ
Substituting the given values, we get:
∠WXY = 180° - 45° - 135°
Simplifying, we get:
∠WXY = 40°
Therefore, the measures of angles in triangle XYZ for scenario A are:
∠ZXY = 45°, ∠WXZ = 135°, ∠WXY = 40°
For scenario B, we have:
∠ZXY = 45°, ∠WXZ = 45°, ∠WXY = 90°
We can see that ∠WXY is already given, so we don’t need to use the fact that the sum of the interior angles of a triangle is 180 degrees to find its measure.
For scenario C, we have:
∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 135°
We can use the fact that the sum of the interior angles of a triangle is 180 degrees to find the measure of ∠WXY.
∠WXY + ∠ZXY + ∠WXZ = 180°
Simplifying, we get:
∠WXY = 180° - ∠ZXY - ∠WXZ
Substituting the given values, we get:
∠WXY = 180° - 45° - 90°
Simplifying, we get:
∠WXY = 55°
Therefore, the measures of angles in triangle XYZ for scenario C are:
∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 55°
For scenario D, we have:
∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 180°
We can see that ∠WXY is already given, so we don’t need to use the fact that the sum of the interior angles of a triangle is 180 degrees to find its measure.
In all four scenarios, we can see that the sum of the interior angles of triangle XYZ is 180 degrees, as expected.
What are the measures of angles in triangle XYZ for the given scenarios A, B, C, and D?
Given
A) ∠ZXY = 45°, ∠WXZ = 135°, ∠WXY = 180°
B) ∠ZXY = 45°, ∠WXZ = 45°, ∠WXY = 90°
C) ∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 135°
D) ∠ZXY = 45°, ∠WXZ = 90°, ∠WXY = 180°