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

1. 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

It is an isosceles triangle.

Because,

AC = CD

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

Now,

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°