Can a quadrilateral have all four angles obtuse (each greater than 90°)?

Class 8Understanding QuadrilateralsQuadrilaterals

ANo, because four obtuse angles would sum to more than 360°
BYes, as long as no angle exceeds 180°
CYes, because quadrilateral angles can total any value
DNo, because at least two angles must always be acute

Step-by-Step Solution

Four obtuse angles would each exceed 90°, giving a total greater than 360°. But quadrilateral angles sum to exactly 360°, so this is impossible.

Answer: A) No, because four obtuse angles would sum to more than 360°

Key idea: Sum of interior angles

**Sum of interior angles of any quadrilateral = 360°.**

Why? Draw one diagonal — it splits the quadrilateral into two triangles. Each triangle has angles summing to 180°. Two triangles → 360°.

More generally: for an n-sided polygon, sum of interior angles = (n − 2) × 180°. For a quadrilateral, n = 4: (4 − 2) × 180° = 360°.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Understanding Quadrilaterals practice questions

More Class 8 Understanding Quadrilaterals practice

Which quadrilateral is defined by having two pairs of adjacent (consecutive) sides equal?Which statement is correct about a rectangle?A trapezium is a quadrilateral with at least one pair of parallel sides. Using this…How many sides does a regular polygon have if each interior angle is 135°?Which of the following is a property common to BOTH a rhombus and a rectangle?