How do you know that the corresponding angle to the right angle is also 90º?

Its because its perpendicular and also because if the angle which is 90 degrees and if it is corresponding to another angle that angle would also be 90 degrees and so if there's and angle missing just look for the corresponding one and that one will be the same degree.

You know if it is a right angle or not because it has straight lines. It has to have to straight lines, making a little box. 
Well, the answer you could put is that the corresponding angle has the same characteristics as it, and you can form a little box at the beginning. ALSO, if you measured with a protractor, you would get exactly 90 degrees.

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