Question

In the adjoining figure, ABCD is a parallelogram and diagonals intersect at point O. Find
(1) Angle CAD
(2) Angle ACD
(3) Angle ADC​

Answer 1

Answer:

in the adjoining figure ABCD is a parallelogram and diagonals intersect at O find angle C A D,angle ACD and angle ADC.. 2. See answers.

Answer 2

Answer:

Given ABCD is a parallelogram.

By considiring the attached figure,

In triangle BCD,

Angle CDB+Angle CBD+angle BCD= 180° [ angle sum property of triangle]

angle BDC= 30°,angle CBD=46°

so, 30°+46°+ angle BCD =180°

76° + angle BCD = 180°

angle BCD = 180°-76°

= 104°

Here, ACD is a straight line

angle AOD+ angle COD = 180° [ By linear pair property]

68°+ angle COD= 180°

angle COD= 180°-68°

= 112°

Now, In Triangle COD,

angle ODC+ angle OCD+angle COD= 180° [ Angle sum property of a Triangle]

30°+ angle OCD+112°=180°

142°+angle OCD=180°

angle OCD=180°-142°

= 38°

angle ACD= 38°

In Triangle BOC,

angle CBO+angle BCO+angle BOC=180° [ angle sum property of a Triangle]

angle AOD= angle BOC=68°(Vertically opposite angle)

46°+angle BCO+68°=180°

114°+ angle BCO=180°

angle BCO=180°-114°

= 66°

Here angle BCO=angle CAD[ Alernate interior angle]

angle CAD=66°

Now In triangle ADC,

angle ADC+angle CAD+ angle ACD=180°[ Angle sum property of a triangle]

angle ADC+66°+38°=180°

angle ADC= 180°-38°

= 76°

a) Angle CAD=66°

b)Angle ACD=38°

c) Angle ADC=76°