Question

descending order of
3. In AABC, BC is produced to D so that
AB = AC=CD. If ZBAC = 720, find the angles
of AABD and arrange its sides in ascending
order of length.
720
B
D
С
98
ICSE Mat​

Answer 1

Answer:

Step-by-step explanation:

∠ABO=37  

o

 

∠ACB=180  

o

−117  

o

=63  

o

 

∠OCB=63/2

BOC=180−37−31.5=180

                                                   68.5

111.5  

o

 

BC>OC>OB (length).

Answer 2

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...

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