Question

The ratio between the three angles of a quadrilateral is 1 : 6 : 2, respectively. The value of the fourth angle of the quadrilateral is 45°. What is the difference between the value of the largest and the smallest angles of the quadrilateral

Answer 1

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= Given that,

= the ratio = 1:6:2

= One angle is 45°.

= Let the angle be x.

= Then, our required angles will be,

= 1x, 6x and 2x.

= We know that,

= The angle sum property of a quadrilateral is 360°.

= Therefore, 1x + 2x + 6x + 45° = 360°

= 9x + 45° = 360°

= 9x = 360° - 45°

= 9x = 315°

= x = 315°/ 9

= x = 35°

= Therefore, the angles will be,

= x = 35°

= 6x = 6 × 35° = 210°

= 2x = 2 × 35° = 70°

= Therefore, the angles are 45°, 35°, 210° and 70°.

= The greatest angle is 210°.

= The smallest angle is 35°.

= Therefore, The difference will be,

= 210° - 35°

= 175°.

= Therefore, the difference between the greatest and the smallest angleis 175°.


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