Answer:
ΔABC are x = 60 degrees, y = 45 degrees, and z = 75 degrees.
Step-by-step explanation:
To solve this problem, we need to identify the angle measures of the triangle ΔABC. The angle measures of a triangle are the degrees of the angles formed by the three sides.
First, we need to find the three angles of the triangle. We can do this by using the fact that the sum of the interior angles of a triangle is always 180 degrees. In this case, the triangle has three angles, so the sum of the angles is 180 degrees.
Let's say the three angles are x, y, and z. We can write this as:
x + y + z = 180
Next, we can use the fact that the sum of the exterior angles of a triangle is always 360 degrees. In this case, the triangle has three exterior angles, so the sum of the angles is 360 degrees.
Let's say the three exterior angles are a, b, and c. We can write this as:
a + b + c = 360
Now, we can use the fact that the measure of an exterior angle is equal to the sum of the measures of the interior angles opposite to it. In other words, a = x + y, b = y + z, and c = x + z.
Substituting these expressions into the equation a + b + c = 360, we get:
x + y + y + z + x + z = 360
Simplifying this equation, we get:
2y + 2z = 360 - x
Now, we can use the fact that the sum of the angle measures of a triangle is always 180 degrees. In this case, the sum of the angle measures is 2y + 2z.
Substituting this expression into the equation x + y + z = 180, we get:
x + 2y + 2z = 180
Simplifying this equation, we get:
x + 2y + 2z = 180
2y + 2z = 180 - x
Solving these two equations simultaneously, we get:
x = 60
y = 45
z = 75
Therefore, the angle measures of the triangle ΔABC are x = 60 degrees, y = 45 degrees, and z = 75 degrees.
Hope this helps!
