Question
Download Solution PDFABCD is a rhombus with ∠ABC = 52°. The measure of ∠ACD is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ABCD is the rhombus.
∠ABC = 52°
Concept:
We know that the rhombus is a parallelogram and in the parallelogram, opposite angles are equal and the diagonal bisects the angle into two equal parts.
The diagonal of a rhombus bisect each other at 90°
Calculation:
ABCD is the rhombus, In which diagonal intersects at 'O' at 90°
In the ΔOCD
∠ODC = 52°/2 = 26°
∠DOC = 90°
We know that the sum of all angle of a triangle is 180°
⇒ ∠ODC + ∠DOC + ∠OCD = 180°
⇒ 26° + 90° + ∠ACD = 180° (∠OCD = ∠ACD)
⇒ ∠ACD = 180° - 116°
⇒ ∠ACD = 64°
∴ The measure of ∠ACD is 64°.
Last updated on Jun 13, 2025
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