Answer:
[tex]\begin{gathered}\large\qquad\qquad\boxed{ \bold{ \: \: \:(b) \: \: 3 \: \: \: }} \\ \end{gathered} [/tex]
Step-by-step explanation:
Given that, RENT is a rectangle such that diagonals RN and ET meet at O.
We know, In rectangle, diagonals are equal and bisects each other.
So, using this property of rectangle, we have:
[tex]\begin{gathered}\sf \implies \:RN = ET \\ \end{gathered} [/tex]
[tex]\begin{gathered}\sf \implies \:\dfrac{1}{2} RN = \dfrac{1}{2} ET \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \implies \:OR = OT \\ \end{gathered} [/tex]
[tex]\begin{gathered}\sf \implies \:2x + 4 = 3x + 1 \\ \end{gathered} [/tex]
[tex]\begin{gathered}\sf \implies \:2x - 3x = 1 - 4 \\ \end{gathered} [/tex]
[tex]\begin{gathered}\sf \implies \: - x = - 3 \\ \end{gathered} [/tex]
[tex]\begin{gathered}\sf\implies \bold{ \: x = 3 }\\ \end{gathered} [/tex]
[tex] \\ [/tex]
[tex] \qquad \qquad \large \underline{ \sf{ \blue{ \pmb{Additional \: Information : }}}} \\ [/tex]
Sum of all interior angles of a convex polygon of n sides is:
[tex]\begin{gathered}\sf \:\qquad \hookrightarrow \: \boxed{ \sf{ \: \:(2n - 4) \times 90\degree \: \: }} \\ \end{gathered} [/tex]
For a regular polygon of n sides, we have a relationship:
[tex]\begin{gathered}\qquad \hookrightarrow \: \boxed{ \sf{ \: \:Exterior \: angle \: = \: \frac{360\degree}{n} \: \: }} \\ \end{gathered} [/tex]
[tex]\begin{gathered}\qquad \hookrightarrow \: \boxed{ \sf{ \: \:n \: = \: \frac{360\degree}{Exterior \: angle} \: \: }} \\ \end{gathered} [/tex]
The smallest interior angle of a regular polygon is 60°.
The largest exterior angle of a regular polygon is 120°.
[tex] \sf{ \pmb{In \: parallelogram : }} \\ [/tex]
[tex] \qquad \bull \: \: \sf{Opposite \: sides \: are \: equal.} \\ [/tex]
[tex] \sf \qquad \bull \: \: {Opposite \: angles \: are \: equal.} \\ [/tex]
[tex] \qquad \sf \bull \: \: {Diagonals \: bisect \: each \: other.} \\ [/tex]
[tex] \qquad \sf \bull \: \: {Sum \: of \: adjacent \: angles \: is \: 180 \degree.} \\ [/tex]
