Question

Can you find the value of x

Answer 1

from your previous posting, you saw that y = 18, that means that the angle 2y + 6 is really 2(18) + 6 or namely 36 + 6 = 42°.

vertical angles, or namely angles across from each other at a junction, are always equal, so if 2y + 6 is 42°, then 8y - 102 is also 42°.

let's recall that a circle has a total of 360°, if we subtract those two vertical angles from a full circle, that'd be 360 - 42 - 42 = 276.

the angle 3x and its vertical angle twin, each take half of that 276° leftover, namely 276 ÷ 2 = 138°.

so now we know that 3x = 138,
`\bf 3x = 138\implies x=\cfrac{138}{3}\implies x=46`