Question
If PAIR and RODS are two rectangles, find $\angle I O D$.
✓
Answer
Since PAIR and RODS are two triangles.
$\angle RIO =90^{\circ}$ $\qquad$ (Corner angle of a rectangle)
In $\triangle RIO$,
$\angle IRO +\angle IOR +\angle RIO =180^{\circ}$ $\qquad$ (Sum of angles of a triangle)
$30^{\circ}+\angle IOR +90^{\circ}=180^{\circ}$
$120^{\circ}+\angle IOR =180^{\circ}$
$\angle IOR =180^{\circ}-120^{\circ}=60^{\circ}$.
$\therefore \angle IOD =90^{\circ}-\angle IOR =90^{\circ}-60^{\circ}=30^{\circ}$.
$\angle RIO =90^{\circ}$ $\qquad$ (Corner angle of a rectangle)
In $\triangle RIO$,
$\angle IRO +\angle IOR +\angle RIO =180^{\circ}$ $\qquad$ (Sum of angles of a triangle)
$30^{\circ}+\angle IOR +90^{\circ}=180^{\circ}$
$120^{\circ}+\angle IOR =180^{\circ}$
$\angle IOR =180^{\circ}-120^{\circ}=60^{\circ}$.
$\therefore \angle IOD =90^{\circ}-\angle IOR =90^{\circ}-60^{\circ}=30^{\circ}$.
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