question_answer

A diagonal of a rectangle is inclined to one side of the rectangle at\[\angle PQS\]. The acute angle between the diagonals is

A)  \[{{90}^{o}}\]                    

B)  \[{{42}^{o}}\]

C)  \[{{48}^{o}}\]                

D)  \[{{38}^{o}}\]

Correct Answer: C

Solution :

Since, \[\Rightarrow \], clearly \[\frac{AO}{OD}=\frac{2}{1}\]. Let diagonals meet at O. Triangle OCB is an isosceles triangle.             \[AO:OD=2:1\]           \[\angle A,\angle B,\angle C\] Hence  \[\angle D\]  \[{{360}^{o}}\]