Three angles 90° in a Quadrilateral

Transcript

Three angles 90° in a QuadrilateralWe answer the question Is it possible to construct a quadrilateral with three angles equal to 90° and the fourth angle not equal to 90°? Let SOME be a quadrilateral with 3 angles 90° Let ∠ S = ∠ O = ∠ E = 90° We need to find ∠ M By Angle sum Property of Quadrilateral Sum of angles of a quadrilateral is 360° ∠ S + ∠ O + ∠ M + ∠ E = 360° Putting values 90° + 90° + ∠ M + 90° = 360° 270° + ∠ M = 360° ∠ M = 360° – 270° ∠ M = 90° Thus, if 3 angles are 90° Then, the last angle is also 90° So, our quadrilateral becomes a rectangle