Answer:
x = 9.8
Step-by-step explanation:
(please refer to attached)
after labeling the picture with all the known information, we can see that
OF = OR = Radius of the circle -----(eq 1)
Consider triangle OFP, by Pythagorean theorem,
OF² = PF²+OP²
r² = 11.5² + 11²
r² = 253.25 -----(eq 2)
Consider triangle ORQ, by Pythagorean theorem,
OR² = RQ²+OQ²
r² = 12.5² + x²
r² = 156.25 + x² ----(eq 3)
equating (eq 2) and (eq 3)
253.25 = 156.25 + x²
x² = 253.25 - 156.25
x² = 97
x = √97
x = 9.8 (nearest tenth)
When you have two parallel lines being cut by a transversal, you can use the next statements for the angles:
The measurement of the angles in green is the same (are congruents)
The measurement of the angles in blue is the same (are congruents)
An angle in green is a complementary angle with an angle in blue. (The addition of the two angles has to be 180º)
You know that:
As the angle 3 is congruent with angle 2:
