Let's assume that angle B is x degrees.
Given that angle A is twice as large as angle B, we can write angle A = 2x degrees.
Also, angle C can be found by subtracting the sum of angles A and B from 180 degrees because the sum of the interior angles of a triangle is always 180 degrees.
So, angle C = 180 - (2x + x) degrees = 180 - 3x degrees.
According to the given information, angle B is 20 more than the sum of angles A and C, so angle B = (2x + (180 - 3x)) + 20 degrees = (200 - x) degrees.
The sum of all the interior angles of a triangle is 180 degrees, so we can write:
A + B + C = 180.
Substituting the values we found for angle A, B, and C, we get:
2x + (200 - x) + (180 - 3x) = 180.
Simplifying the equation, we have:
2x + 200 - x + 180 - 3x = 180.
Combining like terms, we get:
-2x + 380 = 180.
Subtracting 380 from both sides, we have:
-2x = -200.
Dividing both sides by -2, we get:
x = 100.
Therefore, angle B is 100 degrees, angle A is 2x = 2(100) = 200 degrees, and angle C is 180 - 3x = 180 - 3(100) = 180 - 300 = -120 degrees.
However, since angle C cannot be negative, it means there is no valid triangle that satisfies the given conditions.
In a triangle abc anvle a is twice as large as angle B and angle b is 20 more than angle the sum of interior angle of triangle is 180⁰
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