What are the answers for 7-10 this is geometry.

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°.

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