Question

This question seems simple but it's not... been doing it for 3 months and still haven't figured it out so this is last my hope.

The textbook says x=43.6, and it is right when i checked it using substitution.

I just want some working out to see how you would get there.​

Answer 1

Treat the inside shape, that looks like a triangle, as a quadrilateral. Because if you look closely, it actually has 4 sides. Therefore, the angle sum of a quadrilateral, is 360. (you can divide the quadrilateral into two triangles, and then angle sum of triangle = 180 and multiply by 2 = 360).

Hence, summing all the angles:

360° = 44° + (360-166) [angles on a point add up to 360] + (180-(2x+30)) [angles on a straight line add up to 180] + (180-(3x-10))

360 = 44 + 194 + 180 - 2x - 30 + 180 - 3x + 10

360 = 578 - 5x

-218 = -5x

x = 43.6