Mathematics 10 — Exercise 9.1 · Q4

Full question

Central angle DOF=130°. Find angle DEF on the corresponding major arc.

Step-by-step solution

1. The angle at the centre is twice the angle at the circumference standing on the same arc.

2. Substitute the given numbers into the formula.

   $$\frac{130}{2}$$

3. Calculate this operation before combining the remaining terms.

   $$130\times 1=130$$

4. Calculate this operation before combining the remaining terms.

   $$1\times 2=2$$

5. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{130\times 1}{1\times 2}$$

6. Calculate these two products separately.

   $$\frac{130}{2}$$

7. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

   $$\mathrm{GCD}=2$$

8. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{2\times 1}{1\times 2}$$

9. Calculate these two products separately.

   $$\frac{2}{2}$$

10. Show the two divisions explicitly.

    $$\frac{\frac{2}{2}}{\frac{2}{2}}$$

11. Write the reduced fraction.

    $$\frac{1}{1}$$

12. Calculate this operation before combining the remaining terms.

    $$2\times \frac{1}{2}=1$$

13. Calculate this operation before combining the remaining terms.

    $$\frac{1}{1}=1$$

14. Calculate this operation before combining the remaining terms.

    $$65\times 1=65$$

15. Show the two divisions explicitly.

    $$\frac{\frac{130}{2}}{\frac{2}{2}}$$

16. Evaluate the numerator division.

    $$\frac{130}{2}=65$$

17. Evaluate the denominator division.

    $$\frac{2}{2}=1$$

18. Write the reduced fraction.

    $$65\times \frac{1}{1}$$

19. Calculate this operation before combining the remaining terms.

    $$130\times \frac{1}{2}=65$$

20. The required result is shown below. Unit: °

    $$65$$

Answer

The final answer is shown below.