Discussion
The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. What is the difference between the least and the greatest angles of the quadrilateral ?
Answer: D
The difference is 90°.
The angles of a quadrilateral add up to 360°. With the ratio 3 : 5 : 7 : 9:
\[ \begin{aligned} 3 + 5 + 7 + 9 &= 24\ \text{parts} \\ 1\ \text{part} &= 360^{\circ}/24 = 15^{\circ} \\ 9 \times 15 - 3 \times 15 &= 135 - 45 = 90^{\circ} \end{aligned} \]
The angles are 45°, 75°, 105° and 135°. Using 180° (the triangle sum) instead of 360° would halve every angle and give 45°, which is not offered; 60° and 72° do not follow from the ratio.
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