Answer:
7) x = 9°
8) x = 5°
9) x = 10°
10) x = 12°
Explanation:
7) By the angle subtended at the center is twice the angle subtended at the circumference, we have;
∠JLM = ∠JKV = 55°/2 = 27.5°
Similarly;
∠JML = ∠JVK = (18·x + 13)/2 = 9·x + 6.5
By exterior angle theory, we have;
13·x - 2 = 27.5 + 9·x + 6.5 = 9·x + 34
13·x - 9·x = 34 + 2 = 36
4·x = 36
x = 36/4 = 9
x = 9°
8) By the theorem angle formed on the outside of the circle by a tangent and a secant is equal to the difference of the arcs formed in between by the intercept of the tangent and the secant and the circle multiplied by half
Therefore;
8·x + 8 = (1/2) × (170° - (15·x - 1))
8·x + 8 = 85° - 7.5·x + 1/2
8·x +7.5·x = 85° - 8 + 1/2 = 77.5°
15.5·x = 77.5
x = 77.5°/15.5 = 5°
x = 5°
9) ∠TEU = ∠TWV = 175°/2 = 87.5°
∠TUU = ∠TYV = (5·x - 5)/2 = 2.5·x - 2.5
115° = 87.5° + 2.5·x - 2.5 = 90° + 2.5·x
2.5·x = 115° - 90° = 25°
x = 25°/2.5 = 10°
x = 10°
10) The measure of the intercepted arc formed by a chord is equal to twice the measure of the angle the chord forms with a tangent it intersects at the tangent point;
21·x + 18 = 2 × (The supplementary angle to ∠STU)
The supplementary angle to ∠STU = 180° - 45° = 135°
∴ 21·x + 18 = 2 × 135° = 270°
21·x = 270 - 18 = 252
x = 252/21 = 12
x = 12°.
The anoles that changed were the descendants of the anoles studied four years earlier by Losos.
<h3>What is natural selection?</h3>
Natural selection is a term that refers to the evolutionary process that is based on the principle that establishes the survival of the fittest or the preponderance of the law of the strongest in a natural environment without external intervention.
In natural selection, the least fit or weakest individuals perish and their traits are not transmitted to the following generations by not reproducing.
According to the above, it can be inferred that the traits of the weak or less fit organisms studied four years earlier were not transmitted to the following generations, so the organisms studied by Losos four years later are not the same, but the offspring of The originals.
Learn more about natural selection in: brainly.com/question/9830102
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