Mathematics 10 — Exercise 9.1 · Q2

Full question

AB and AC are tangents from A. Angle BAC=65°. Find angle ABC.

Step-by-step solution

1. Tangents drawn from the same external point are equal: AB=AC. Thus base angles ABC and BCA are equal.

2. Subtract 65° from 180°, then divide the remaining angle sum equally by 2.

3. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 65=-65$$

4. Substitute the given numbers into the formula.

   $$\frac{180-65}{2}$$

5. Calculate this operation before combining the remaining terms.

   $$180-65=115$$

6. Calculate this operation before combining the remaining terms.

   $$115\times 1=115$$

7. Calculate this operation before combining the remaining terms.

   $$1\times 2=2$$

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

   $$\frac{115\times 1}{1\times 2}$$

9. Calculate these two products separately.

   $$\frac{115}{2}$$

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

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

11. Calculate these two products separately.

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

12. Calculate this operation before combining the remaining terms.

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

13. Calculate this operation before combining the remaining terms.

    $$115\times \frac{1}{2}=\frac{115}{2}$$

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

    $$\frac{115}{2}$$

Answer

The final answer is shown below.