Maths-
General
Easy

Question

Which statement is true by angle addition postulate?
a. 𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐴𝑂𝐷
b. 𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐵𝑂𝑃 = 𝑚∠𝐴𝑂𝑃
c. 𝑚∠𝐵𝑂𝑃 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐵𝑂𝐷

The correct answer is: 2 is true


    • Step by step explanation: 
      • Step 1:
      • given

    𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐴𝑂𝐷
    From above figure, it is clear that
    𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐶𝑂𝐷 does not make complete angle.

     ∴ 𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐴𝑂𝐷

    • Step 2: 

    𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐵𝑂𝑃 = 𝑚∠𝐴𝑂𝑃
    From above figure, it is clear that

    𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐵𝑂𝑃 = 𝑚∠𝐴𝑂𝑃

    ∴ 𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐵𝑂𝑃 = 𝑚∠𝐴𝑂𝑃

    • Step 3:

    𝑚∠𝐵𝑂𝑃 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐵𝑂𝐷
    From above figure, it is clear that

    𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐶𝑂𝐷 + 𝑚∠𝐶𝑂P = 𝑚∠𝐴𝑂𝐷.

     ∴ 𝑚∠𝐵𝑂𝑃 + 𝑚∠𝐶𝑂𝐷 = 𝑚∠𝐴𝑂

    • Final Answer:
    Hence, statement 2 is true.