Question

3. In triangle ABC ,BC is produced to D so that
AB= AC=CD. If angle BAC = 72°, find the angles
of triangle ABD​

Answer 1

Answer:

90 degree because lt is a height

Answer 2

ANSWER:

In the above ∆ABD

∆ABC is a isosceles triangle

Because ,

AB = AC

We know that in an isosceles triangle equal sides 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° = 180°

2x° = 180° - 72°

2x° = 108°

x° = 108°/2 = 54°

x° = 54° = angle ABC = angle ACB

Now, going to ∆ADC

It is an isosceles triangle

Because,

AC = CD

In an isosceles triangle equal sides 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 angle sum property

131° + y° + y° = 180°

2y° = 180° - 131°

2y° = 49°

y° = 49°/2

y° = 24.5° = angle CAD = angle CDA

Now,

The angles of ∆ABD

angle ABC = 54°

angle DAB = angle CAB + angle CAD

angle DAB = 72° + 24.5° =96.5°

angle ADB = 24.5°