Question

The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?

Answer 1

A1=40

Explanation:

Let A1,A2,A3 be the angles of the triangle

We know, A1+A2+A3 = 180 -------(1)
given A2=2(A1) ------(2)
A3= A1+20 --------(3)

Putting 2 & 3 in 1 , we get

A1+2(A1)+A1+20=180

`=>4(A1)=160`

A1=40

Answer 2

`40`

Explanation:

Let x be first interior angle of the triangle. Then, second and third interior angles will be `2x` and `x+20`, respectively.

The sum of the measures of the interior angles of a triangle is 180 degrees:
`color(white)(xx)xcolor(blue)(+)2xcolor(blue)(+)x+20=180`
`=>4x+20=180`
`=>4x+20color(red)(-20)=180color(red)(-20)`
`=>color(red)(1/4*)4x=color(red)(1/4*)160`

`=>x=40`