Question

Match the columns.

Column I		Column II
I	The number of lines of symmetry of a square is	P	$60^{\circ }$
II	The number of lines of symmetry of a square is	Q	$4^{\circ }$
III	Each angle is an equilateral triangle is	R	$45^{\circ }$
IV	The sum of an angle and one - third of its supplementary angle is $90^{\circ }$. What is the angle	S	$2^{\circ }$

• A. I—Q; II—R; III—S; IV—P
• B. I—R; II—P; III—S; IV—Q
• C. I—P; II—Q; III—S; IV—R
• D. I—Q; II—S; III—P; IV—R

Answer 1

Answer: (D)

I. A square has 4 lines of symmetry ...(Q)
II. A rectangle has 2 lines of symmetry the lines of symmetry in a rectangle cut its opposite sides into equal parts...(S)
III. In geometry, an equilateral triangle is a triangle in which all three sides are equal that is, all three internal angles are also congruent to each other and are each $60^{\circ }$....(P)
IV. Let the angle be $x^{\circ }$ It supplementary angle $=180^{\circ }-x$ According to statement,
$x+\frac{1}{3}\left(180^{\circ }-x\right)=90^{\circ }$
$\Rightarrow x+\frac{180^{\circ }}{3}-\frac{x}{3}=90^{\circ }$
$\Rightarrow x+60^{\circ }-\frac{x}{3}=90^{\circ }$
$\Rightarrow \frac{3x-x}{3}=30^{\circ }$
$\Rightarrow 2x=90^{\circ }$
$x=45^{\circ }$....(R)