Calculate the values of x, y, and z.
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Calculate the values of x, y, and z.
Angle Y complements 180 and we can calculate it since we know the adjacent angle.
Let's calculate it as follows:
Now that we found angle Y, we can calculate angle X since we have the other two angles in the same triangle: 72 and 75.
We can calculate angle Z since we have two angles in the triangle: 25 and 105
The sum of angles in a triangle is 180, so we'll calculate Z as follows:
x = 33, y = 75, z = 50
Indicates which angle is greater
Interior angles are inside the triangle shape. Exterior angles are formed when you extend a side beyond the triangle. In this problem, 105° is exterior because it's outside the triangle boundary.
Angles y and 105° form a linear pair on a straight line. Since they must add to 180°, we get:
Not always! Start with angles that have direct relationships first. Here, find y using the linear pair, then use y to find x, and finally find z.
Double-check your work! You may have confused interior and exterior angles or made a calculation error. Each triangle's interior angles must always sum to exactly 180°.
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