(a) The diagram, = IWYI = IXZI and < WXY = 80\(^o\). What is the size of < XWZ? (b) A man was charged 2 kobo per month for every N1.00 he borrowed from a ba...

Answer Details

(a) Finding \(\angle XWZ\)

\(WXYZ\) is a quadrilateral inscribed in the circle (a cyclic quadrilateral) with vertices in order \(W, X, Y, Z\). Its diagonals are equal: \(|WY| = |XZ|\), and \(\angle WXY = 80^{\circ}\).

Step 1: Interpret the equal diagonals. A cyclic quadrilateral whose diagonals are equal is an isosceles trapezium. From the diagram, side \(WX\) is parallel to side \(ZY\) (\(WX \parallel ZY\)), and the legs \(WZ\) and \(XY\) are the equal sides.

Step 2: Apply the base-angle property. In an isosceles trapezium the two angles standing on the same parallel side are equal. Here \(\angle XWZ\) (at \(W\)) and \(\angle WXY\) (at \(X\)) both stand on the base \(WX\), so they are equal:

\[ \angle XWZ = \angle WXY = 80^{\circ} \]

Check (cyclic quadrilateral): The opposite angles are then \(\angle WZY = \angle XYZ = 180^{\circ} - 80^{\circ} = 100^{\circ}\), and \(80^{\circ} + 100^{\circ} = 180^{\circ}\), confirming that opposite angles are supplementary.

\(\angle XWZ = 80^{\circ}\).

(b) Rate of interest per annum

The man is charged \(2\) kobo per month for every \(N1.00\) borrowed. Since \(N1.00 = 100\) kobo, the monthly interest on \(N1.00\) is:

\[ \text{monthly rate} = \frac{2\text{ kobo}}{100\text{ kobo}} \times 100\% = 2\%\text{ per month} \]

There are \(12\) months in a year, so:

\[ \text{rate per annum} = 2\% \times 12 = 24\% \]

The interest was charged at 24% per annum.