[SPM Mathematic Question] How to find the value of x?

Mathematic Question

  1. Dalam Rajah 3, CDE ialah tangen kepada bulatan berpusat O pada titik D .
    In Diagram 3 , CDE is a tangent to the circle with the centre O at point D.
    Cari nilai x.
    Find the value of x.
    A 15^{\circ}
    C 70^{\circ}
    B 35^{\circ}
    D 85^{\circ}

Mathematics Solution

Let the small angle beside x be called as y.

Using the Circle’s Theorem, the angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle’s circumference

1. Angle at AOD (center) should be twice the angle at ABD, hence Angle ABD = 35°

2. Outer angle of AOD = 360° - 70° = 290°.

3. The quadrilateral, ABDO has a total internal angle of 360°.

4. y (small angle beside x) is equal to 360° - 290° - 35° - 15° = 20°

5. Since CDE is a tangent to the circle, Angle ODE = 90°. Therefore, x = 90° - 20° = 70°.

Therefore, the answer is C. 70°.