Question

in a right angled ΔABC, AC is hypotenuse and other two sides are of length 12m and 9m . X is a point outside the triangle such that XA=20m and XC=25 M.  find the measure of angle XAC.

Answer 1

AC = √(12² + 9²) = 15m
In triangle AXC, AX = 20, AC = 15 .
AX² + AC² = 20² + 15² = 625 = 25² = XC²
Hence angle AXC is a right angle.
[Hope you meant angle AXC and not angle XAC]

If you want angle XAC, use trigonometry.