Mathematics 10 — Exercise 9.2 · Q3 (iii), y

Full question

XY is tangent at Y and XOY=62°. Find y=OXY.

Step-by-step solution

1. A radius is perpendicular to the tangent at its point of contact, so the contact angle is 90°.

2. The three angles of a triangle add to 180°. Subtract both known angles.

3. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 90=-90$$

4. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 62=-62$$

5. Substitute the given numbers into the formula.

   $$180-90-62$$

6. Calculate this operation before combining the remaining terms.

   $$180-90-62=28$$

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

   $$28$$

Answer

The final answer is shown below.