Explanation:
remember, the sum of all angles in a triangle is always 180°.
now let's consider the white, "cut-out" triangle on the left side.
the purple one angles at the top and bottom corner are 45°.
the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.
so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).
and that means that the third white angle is
180 - 45 - 45 = 90°.
and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.
360 = 90 + 3x
270 = 3x
x = 90°
3x = 270°