- A93°
- B97°
- C83°
- D263°
Step-by-Step Solution
The angles of a quadrilateral add up to .
Answer: C) 83°
In quadrilateral ABCD, ∠A = 78°, ∠B = 104° and ∠D = 95°. Find the angle marked at C.
Class 8Understanding QuadrilateralsQuadrilaterals
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°.
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°.
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