Answer :

Given: ΔXYZ, XYZ = 90° and

To prove: YXZ = 60°

The figure for the above question is as shown below,

Given ΔXYZ is a right - angled triangle, now applying the properties of the triangle,

We know

Now when θ = XZY, XY is the opposite side and XZ is the hypotenuse, then the above equation becomes,


Equating equation (i) and (ii), we get


Hence θ = 30°

Or XZY = 30°….(iii)

Now in ΔXYZ,

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

XYZ + XZY + YXZ = 180°

Substituting given value and value from equation (iii) in above equation we get

90° + 30° + YXZ = 180°

YXZ = 180° - 90° - 30°

YXZ = 60°

Hence proved

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