Question

I’m confused on this one

Answer 1

∠1, ∠2, and ∠3 add up to one full turn, or 360°. We can write this fact as the equation

∠1 + ∠2 + ∠3 = 360

∠1 is given to us as a right angle - 90° - and the values ∠2 and ∠3 are given in the question, so we can rewrite our equation with that information as

90 + (x - 7) + 2x = 360

Which we can then solve for x:

x - 7 + 2x = 270 (subtract 90 from both sides)

3x - 7 = 270 (combine like terms)

3x = 277 (add 7 to both sides)

x = 277/3 = 92 1/3 (divide both sides by 3)

Since ∠3 = 2x, we can multiply our result by 2 to find that ∠3 = 2 x (92 1/3) = 184 2/3°

Answer 2

All central angles of a circle add to 360 deg.

m<1 = 90 since <1 is a right angle.

m<1 + m<2 + m<3 = 360

90 + x - 7 + 2x = 360

3x + 83 = 360

3x = 277

x = 277/3

m<3 = 2x = 277/3 * 2 = 554/3 = 184 2/3