Question

How do I find angle A?

Answer 1

so, we know angle at B is 42°, and that the angle at A is 5x +6.

now, notice, the segment BCD is really just a flat-line, namely it has an angle atop of 180°, and notice, the exterior angle is 8x, and the interior angle, we dunno what it is.

however, we know that that exterior angle and the interior angle are siblings, they're both "linear angles", namely they both lie on a flat-line, and therefore, whatever the angle at C is, it must add up to 180° with 8x, therefore, C + 8x = 180, or C = 180 - 8x.

now, recall that all interior angles in a triangle, add up to 180°, therefore


`\bf \stackrel{A}{5x+6}~~+~~\stackrel{B}{42}~~+~~\stackrel{C}{180-8x}~~=~~180 \\\\\\ -3x+228=180\implies 48=3x\implies \cfrac{48}{3}=x\implies 16=x`

so the angle at A will be 5(16) + 6.