3. In AABC, BC is produced to D so that AB=AC=CD. If angle BAC=72, find the angles of angle A BD and arrange its sides in asc

Question

3. In AABC, BC is produced to D so that
AB=AC=CD. If angle BAC=72, find the angles
of angle A
BD and arrange its sides in ascending
order of length​

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Bella 2 weeks 2021-09-10T15:39:51+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-10T15:41:45+00:00

    Step-by-step explanation:

    In the above ∆ABC.

    ∆ABC is an isosceles triangle.

    Because,

    AB=AC

    We know that in an isosceles triangle equal sides are opposite angles are also equal.

    Now,

    Let angle B in ∆ABC be x.

    Then,

    angle B = angle C

    x° = x°

    using angle sum property

    72° + x° + x°

    2x° = 180° – 72° = 108°

    x° = 108°/2 = 54°

    x° = 54° = angle ABC

    Now, going to ∆ADC.

    It is an isosceles triangle.

    Because,

    AC = CD

    We know that in an isosceles triangle equal sides are opposite angles are also equal.

    Now,

    angle CAD = angle CDA

    Let angle CAD = y°.

    y° = y°

    Taking only ∆ABC extending the line BC to CD.

    using the property

    exterior angle = sum of two interior opposite angles.

    angle ACD = angle CAB + angle ABC

    angle ACD = 72° + 59°

    angle ACD = 131°.

    Using the sum property

    131° + y° + y° = 180°

    2y° = 180° – 131° = 49°

    y° = 49°/2 = 24.5° = angle CAD = angle CDA

    Now,

    angle ABC = 54°

    angle DAB = angle CAB + angle CAD

    angle DAB = 72° + 24.5° = 96.5°

    angle ADB = 24.5°

    Hope it helps you…

    Thank you …

    Please mark it as brainliest as it take so much effort…. please…

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