In a triangle abc anvle ais twice as large as angle B and angle b is 20 kore than angle tge sum of interior angle of triangle is 180⁰

Answer 1

Let's denote angle A as x, angle B as y, and angle C as z.

Given that angle A is twice as large as angle B, we have the equation:

x = 2y

Also, angle B is 20 degrees more than the sum of angles A and C:

y = x + z + 20

We also know that the sum of the interior angles of a triangle is 180 degrees:

x + y + z = 180

Using the first equation, we can substitute x in terms of y in the second equation:

2y = y + z + 20
y = z + 20

Now we have two equations with two unknowns:

x = 2y
y = z + 20

Substituting these equations into the sum of the interior angles equation:

2y + y + z = 180
3y + z = 180

We can substitute y = z + 20 into this equation:

3(z + 20) + z = 180
4z + 60 = 180
4z = 120
z = 30

Substituting z = 30 into y = z + 20:

y = 30 + 20
y = 50

Finally, using x = 2y:

x = 2(50)
x = 100

So the triangle has angles A = 100, B = 50, and C = 30.