Question

in the given figure ABCD is a rhombus and angle ACB is 45 degree find the angle ADC​

Answer 1

Answer:

135°

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:-

in the given figure ABCD is a rhombus and angle ACB is 45 degree

To find:-

find the angle ADC

Solution:-

Given that:

ABCD is a rhombus

AC and BD are the two diagonals

we know that

In a rhombus the diagonals perpendicular bisectors to each other

angle COD = angle BOC = angle AOB =

angle DOA = 90°

Now, In ABCD rhombus ,

AD || BC and AC is a transversal then

angle ACB =angle CAD

(alternative interior angles)

and

angle COD = 90°

Now,

In ∆AOD,

angle ADO + angle CAD + angle AOD = 180°

(The sum of all angles in a triangle is 180°)

=>angle ADO +45°+90°=180°

=>angle ADO+135°=180°

=>angle ADO= 180°-135°

=>angle ADO = 45°

=>angle ADB = 45°

and in ∆ABC ,

AB = BC =>angle BAC = angle BCA

(angles opposite to equal sides are equal)

angle BAC = angle BCA =45°

in ∆ABC

angle BCA+angle BAC+angle ABC = 180°

=>45°+45°+angle ABC = 180°

=>angle ABC +90°= 180°

=>angle ABC = 180°-90°

=>angle ABC = 90°

we know that

Opposite angles are equal in a rhombus

=>angle ABC = angle ADC

angle ADC = 90°

Answer:-

Angle ADC for the given problem is 90°

Used formula:-

• angles opposite to equal sides are equal
• Opposite angles are equal in a rhombus
• Opposite sides are equal in a rhombus