What are the measures of the marked angles? a. 19 ° b. 27 ° c. 38 ° d. 90 °

This is an incomplete question, the image is shown below.

Answer : The correct option is, (a) 19°

Step-by-step explanation:

Opposite angles : These are the angles in which a pair of parallel lines are cut by tranversal then the two angles share the same corner.

Opposite angles are also congruent angles, that means they are equal.

As we know that the opposite angles are equal.

And, (3x - 8)°  & (2x + 1)° are alternate interior angles.

Thus, the expression will be:

(3x - 8)  = (2x + 1)

3x - 8  = 2x + 1

3x - 2x = 8 + 1

x = 9

(3x - 8)°  & (2x + 1)°

(3(9) - 8)°  & (2(9) + 1)°

19° & 19°

Therefore, the measures of the marked angles is, 19°

The answer would be option 4

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