Question

Circle P has tangents XY and ZY and chords WX and WZ. The measure of angle ZWX=70 degrees. What is the measure in degrees of angles XYZ?

Answer 1

`angleXYZ = 40^@`

Explanation:

We are given:

`angleZWX = 70^@`

This means that the central angle is:

`angleZPX = 140^@`

The radii of the central angle form right angles with the tangents:

`anglePZY = anglePXY = 90^@`

`PZYX` forms a quadrilateral, therefore, the some of the internal angles are:

`360^@= angleZPX + anglePZY + anglePXY + angleXYZ`

Substituting in the values:

`360^@= 140^@ + 90^@ + 90^@ + angleXYZ`

`angleXYZ = 40^@`