Step 1: Recall properties of a rectangle
A rectangle is a quadrilateral with:
- Opposite sides equal and parallel
- All interior angles equal
Step 2: Use angle sum property of quadrilateral
Sum of all interior angles of a quadrilateral = 360\degree
In a rectangle, all 4 angles are equal. So:
\[
\text{Each angle} = \frac{360\degree}{4} = 90\degree
\]
Step 3: Evaluate options
(A) 60\degree $\Rightarrow$ Incorrect
(B) 30\degree $\Rightarrow$ Too small for rectangle
(C) 45\degree $\Rightarrow$ Diagonal halves form these, not corners
(D) 90\degree $\Rightarrow$ Correct
\[
\boxed{\text{Correct Answer: (D) 90\degree}}
\]
Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $ (\vec{AB}-\vec{BC})+(\vec{AD}-\vec{DC})=k \vec{FE} $, then k is equal to
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.