The ratio between the three angles of a quadrilateral is 13 : 9 : 5 respectively. The value of the fourth angle of the quadrilateral is 36∘C. What is the difference between the largest and the second smallest angles of the quadrilateral?
The ratio between the three angles of a quadrilateral is 13 : 9 : 5 respectively. The value of the fourth angle of the quadrilateral is 36∘C. What is the difference between the largest and the second smallest angles of the quadrilateral?
A104°
B 108°
C72°
D 96°
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Corect answre is: 96°
Explanation:
Let the three angles of quadrilateral be
\(13x^∘, 9x^∘,\text{ and }5x^∘ \text{ respectively.}\)
\(\text{Therefore, } 13x + 9x + 5x = 360 - 36\)
\(\implies 27x = 324 \implies x = \frac{324}{27} =12\)
Therefore, Required difference
\(=13x - 5x = 8x = 8\times \text{12 }= 96^∘\)
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