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?
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?
A$165^∘$
B $140^∘$
C$175^∘$
D$150^∘$
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Correct answer is: \(175^∘\)
Explanation:
Sum of the angles of quadrilateral = \(\Large 360 ^{\circ}\)
\(\implies x + 6x + 2x + 45 = 360\)
\(\implies 9x = 360 - 45 = 315 \)
\(\implies x = \Large \frac{315}{9} =35\)
Therefore, Required difference = \(6x - x = 5x\)
\(= \Large 5 \times 35 - 175 ^{\circ}\)
\(= \Large 175 ^{\circ}\)
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