Question

Three angles for four different quadrilaterals have been given. Which one of the following is a convex quadrilateral?

• A. 30°, 40°, 95°
• B. 10°, 20°, 140°
• C. 45°, 50°, 65°
• D. 5°, 16°, 165°

Answer 1

The correct option is D 5°, 16°, 165°

A polygon with all interior angles less than 180° is a convex polygon. First we have to find the fourth angle in all the given quadrilaterals.

Fourth angle in option (a) = 360°- (30° + 40° + 95°) = 360° - 165° = 195°
Fourth angle in option (b) = 360°- (45° + 50° + 65°) = 360° - 160° = 200°
Fourth angle in option (c) = 360°- (5° + 16° + 165°) = 360° - 186° = 174°
Fourth angle in option (d) = 360°- (10° + 20° + 140°) = 360° - 170° = 190°

Only in option (c) we have all the interior angles less than 180°.