The measure of angle XYZ is 66.4°.
Step-by-step explanation: We are given to find the size of the angle XYZ in the right-angled triangle shown.
We see from the figure that in triangle XYZ,
m∠YXZ = 90°, XY = 6 cm and YZ = 15 cm.
For the acute angle XYZ, XY is the base and YZ is the hypotenuse.
So, we must have
Thus, the required measure of angle XYZ is 66.4°.