I think that x would be 1.5.
6 = 4x, 6/4 = 1.5, so 1/5 = x
30 + 4x + 2 + 180 - (8 + 6x) = 180;The sum of all angles in a triangle is 180
32 + 4x - 8 - 6x = 0
2x = 24
x = 12
Bolded part, explanation: On a straight line, the sum of all angles is 180 degrees. We have the value of outside the triangle, the exterior angle, which, when is added with interior angle, gives 180 degrees. So we substract 8 + 6x from 180, that's the third angle in a triangle.
where is your triangle mate??
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You're looking for a number <em>w</em> such that the numbers
{1 + <em>w</em>, 7 + <em>w</em>, 15 + <em>w</em>}
form a geometric sequence, which in turn means there is a constant <em>r</em> for which
7 + <em>w</em> = <em>r</em> (1 + <em>w</em>)
15 + <em>w</em> = <em>r</em> (7 + <em>w</em>)
Solving for <em>r</em>, we get
<em>r</em> = (7 + <em>w</em>) / (1 + <em>w</em>) = (15 + <em>w</em>) / (7 + <em>w</em>)
Solve this for <em>w</em> :
(7 + <em>w</em>)² = (15 + <em>w</em>) (1 + <em>w</em>)
49 + 14<em>w</em> + <em>w</em> ² = 15 + 16<em>w</em> + <em>w</em> ²
2<em>w</em> = 34
<em>w</em> = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
I’m sure it’s only A/E, apologies if wrong