Question

In a pentagon, if two interior angles are ${140}^{\circ }$ and ${160}^{\circ }$, and the remaining angles are in the ratio 1 : 3 : 4, then its smallest angle measures ____ .

• A. 120°
• B. 90°
• C. 30°
• D. 20°

Answer 1

The correct option is C

30°

Let the three angles be x°, 3x° and 4x°

Sum of interior angles of a polygon with n sides = (2n - 4) x 90°

140° + 160° + x° + 3x° + 4x° = (10 - 4) x 90°

8x° + 300 = 540

8x° = 240

x = 30°

The smallest angle = 30°