The measure of the angle X in the triangle is 65 degrees.
How to find the measure of angle in a triangle?
The measure of the angle in the triangle can be found using cosine law for triangle.
Therefore,
x² = y² + z² - 2yz cos X
Hence,
410² = 450² + 210² - 2(450)(210) cos X
168100 = 202500 + 44100 - 189000 cos X
168100 = 246600 - 189000 cos X
168100 - 246600 = - 189000 cos X
- 78500 = - 189000 cos X
cos X = - 78500 / - 189000
cos X = 0.41534391534
X = cos⁻¹ 0.41534391534
Therefore,
X = 65.4617896691
X = 65 degrees.
Note: The complete question is to find the angle X