Geometry Practice Test 4

Question : 30 of 40

Marks: +1, -0

The ratio between the three angles of a quadrilateral is 3 : 5 : 9 respectively. The value of the fourth angle of the quadrilateral is 71°. What is the difference between the
largest and the smallest angles of the quadrilateral?

82°
106°
102°
92°
None of these

Validate

Solution:

Sum of four angles of quadrilateral = 360°
Ratio between three angles = 3x, 5x, 9x
Fourth angle = 71°
360° − 71° = 289°
Sum of three angles = 289°
3x + 5x + 9x= 289°
17x = 289°
x =

{289°}/{17}

= 17°
Angles ⇒ 3x = 3 × 17 = 51°
5x = 5 ×17 = 85°
9x = 9 ×17 = 153°
Difference between the largest and the smallest 153° − 51° = 102°

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