Question

ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.

Answer 1

Answer:

27 degrees

Step-by-step explanation:

angle ABD = 1/2 angle ABC = 63 degrees

angle ABD = angle BDC since CD is parallel to AB and BD acts as a transversal so these are interior alternate angles

Now angle DOC + angle OCD + angle ODC = 180 degrees by angle sum property

90 + angle OCD + 63 = 180

therefore angle OCD = 27 degrees

angle OCD = angle ACD

So angle ACD = 27 degrees

Answer 2

Given,

$ABCD$ is a rhombus with angle $ABC= 126^{0}$

Rhombus: A rhombus is a quadrilateral whose four sides all have the same length.

All interior add up to $360$ degrees

The opposite sides of the rhombus are equal and side angles are supplementary.

Now,

From the diagram,

∠ $ABC+$  ∠ $BCD$ $= 180$

$126+c=180\\c= 180-126\\c= 54$

∠ $BCD =$  ∠ $ACB+$   ∠$ACD$

From the diagram

∠ $ACB=$  ∠$ACD$

So,

Angle $ACD=angle\frac{BCD}{2}$

So, ∠$ACD$ $= \frac{54}{2}$

$=27$

Therefore, the value of  ∠$ACD$ is $27^{0}$.