Quadrilateral Angles — Ratio to Actual Measure: Angles of a quadrilateral are in the ratio 3 : 4 : 5 : 8. Find the smallest angle (in degrees).

Introduction / Context:The interior angles of any quadrilateral sum to 360°. When a ratio is given, convert the ratio to parts, find the value per part, and multiply by each term to get actual angles. This checks comfort with ratio scaling and polygon-angle sums.

Given Data / Assumptions:

• Angle ratio: 3 : 4 : 5 : 8
• Sum of interior angles of quadrilateral = 360°

Concept / Approach:Total parts = 3 + 4 + 5 + 8 = 20. One part equals 360° / 20 = 18°. The smallest angle corresponds to the smallest ratio term, which is 3 parts. Multiply to obtain the measure.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 40°, 36°, 18° do not match 3 parts at 18° each.
• 72° is the second-smallest (4 parts), not the smallest.

Common Pitfalls:

• Using triangle sum (180°) instead of quadrilateral sum (360°).

Final Answer:54°.