Question

ABCD is a rhombus with angle ABC equal to 126°. Find measure of angle ACD.
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Answer 1

Answer:

54/2

Step-by-step explanation:

As in rhombus Opp. sides are parallel so in rhombus abcd AB is parallel to CD so angle ABC + angle BCD =180

so,126+x=180

so, x=180-126

=54

as diagonals of rhombus bisect opp. angle so angle ACD=54/2

=27

Answer 2

Given,

ABCD is a rhombus with ∠ABC = 126°.

To Find,

Measure of ∠ACD.

Solution,

We know that,

ABCD is a rhombus

∴ ∠ABC + ∠BCD = 180°                   ( Linear Pair)

⇒ ∠BCD = 180° – 126° = 54°

Since AC is the diagonal of rhombus ABCD,

∠ACD = (½) ∠BCD ( In a rhombus, a diagonal divides an angle into 2 equal angles)

⇒ ∠ACD = (½) × 54° = 27°

Hence, the measure of the angle ACD is 27°.