Erin says the first step is to set Latex: 2x+7 2 x + 7 equal to Latex: 5x-2\textsf{.} Antonio says the first step is to set Latex: 2x+7 2 x + 7 plus Latex: 5x-2 5 x − 2 equal to Latex: 180\textsf{.} Choose either Erin's or Antonio's statement and explain why it is correct or incorrect. If the statement is correct, explain how you know it's correct. If the statement is incorrect, explain why it's wrong. If you were to solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure you include all steps needed to solve for Latex: m\angle A\textsf{.}

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

The first option would be correct if it were one half and not one