Question

The following figure is a rhombus. Find the values of the unknowns x, y and z.

• A. $x={90}^{\circ },y={60}^{\circ }andz={60}^{\circ }$
• B. $x={90}^{\circ },y={90}^{\circ }andz={90}^{\circ }$
• C. $x={30}^{\circ },y={60}^{\circ }andz={60}^{\circ }$
• D. $x={90}^{\circ },y={30}^{\circ }andz={30}^{\circ }$

Answer 1

The correct option is A $x={90}^{\circ },y={60}^{\circ }andz={60}^{\circ }$



In rhombus ABCD, diagonals AC and BD bisect each other right angles.
$\therefore x={90}^{\circ }$
In $\Delta OCD$,
$\angle COD+\angle OCD+\angle ODC={180}^{\circ }\Rightarrow {90}^{\circ }+{30}^{\circ }+y={180}^{\circ }\Rightarrow y={180}^{\circ }-{120}^{\circ }={60}^{\circ }\therefore y={60}^{\circ }$
$\because CD||AB$, BD is the transversal
$\therefore$ y = z (Alternate interior angles are equal)
$\therefore z={60}^{\circ }$
Hence, $x={90}^{\circ },y={60}^{\circ }andz={60}^{\circ }$