The measure of $$\angle$$​OQR = 48°, Point V lines on OQ, VT|| QR and S is a point in the interior of $$\angle$$​ OQR such that V, S and T are collinear and S lies in between V and T. P is also a point on OQ, such that P lies in between O and V, and m$$\angle$$​PST = 120°. What is the measure of the complement of $$\angle$$​ QPS ?

Correct option is C

Given:

​$$\angle OQR = 48°$$​​

Point V lines on OQ

VT|| QR

S is a point in the interior of \angle OQR such that V, S and T are collinear

 P is also a point on OQ, such that P lies in between O and V

​$$m\angle PST$$​= 120°

Formula Used:

Sum of complementary angles =$$90^o$$​​

Sum of angles of a triangle =$$180^o$$​​

Solution:

The given figure is shown below:

​$$\angle PVS = \angle = OQR = 48^o$$​ (Corresponding angles)

​$$\angle PSV =180^0 - 120^0 = 60^o$$​​

​$$\angle QPS = 180^o - (60^o + 48^o )$$      (Angle sum property)​

​$$= 180^o - 108^o$$​​

= $$72^o$$​​

Complementary angle of $$\angle QPS = (90^o - 72^o) = 18^o$$​​