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13 June, 05:09

What is the measure of arc AD?

Angle ABD measures (4x + 10). Angle ACD measures

(5x - 2)

GO

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Answers (1)
  1. 13 June, 05:22
    0
    116°

    Step-by-step explanation:

    Given that:

    ∠ ABD measures (4x + 10)

    ∠ ACD measures (5x - 2)

    Then

    ∠ABD = ∠ACD (rule : angle by same chord AD)

    ∠ABD = (4x + 10) °

    ∠ACD = (5x - 2) °

    so we can as well say that:

    (4x + 10) ° = (5x - 2) °

    4x - x = - 10 - 2

    - x = - 12

    x = 12

    ∠ABD = (4x + 10) °

    = (4 * 12 + 10) °

    = 58°

    ∠ACD = (5x - 2) °

    = (5 * 12 - 2) °

    = 58°

    ∠AOD = 2∠ABD = 2∠ACD (since angle by arc AD at center is twice the angle by same arc AC in other arc segment)

    ∠AOD = 2 * 58°

    ∠AOD = 116°

    Measure of arc AD = 116°
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