Q is the centre of a circle and ZXWQ is a parallelogram, where X is a point on the minor arc ZW and Z, W also lie on the circle. What is the measure of \(\angle ZQW\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120°
QZ and QW are radii, and they are two adjacent sides of the parallelogram. A parallelogram with two equal adjacent sides is a rhombus, so all four sides equal the radius \(r\).
QZ \(=\) ZX \(=\) XW \(=\) WQ \(=r\)
QX is also a radius, so \(\triangle QZX\) has all three sides \(r\): it is equilateral and \(\angle ZQX=60^\circ\)
In the same way \(\triangle QXW\) is equilateral and \(\angle XQW=60^\circ\)
\(\angle ZQW=60^\circ+60^\circ=120^\circ\)
