If the angles of a quadrilateral are $4 x °, 2 x + 10 °, 3 x + 20 °, x - 20 °$ , then find the angles.

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Solution

We know that the sum of the angles of a quadrilateral is $360 °$
i.e.
$4 x ° + 2 x + 10 ° + 3 x + 20 ° + x - 20 ° = 360 ° \Rightarrow 10 x + 10 ° = 360 ° \Rightarrow x + 1 = 36 \Rightarrow x = 35$
Now,
$4 x = 4 \times 35 = 140 ° 2 x + 10 = 2 \times 35 + 10 = 80 ° 3 x + 20 = 3 \times 35 + 20 = 125 ° x - 20 = 35 - 20 = 15 °$
Hence, the angles are $140 °, 80 °, 125 °, 15 °$ .

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