Question

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

Answer 1

Question:

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

To find:

$\bigstar To \: find \: the \:measure \: of \: \angle ACD$

Answer:

$The \: measure \: of \: the \: \underline{ \: \underline{\: \sf \pink{\bold{\angle ACD \: is \: 27°}}\:} \: } .$

Given:

$\bigstar \angle ABC = 126°$

Step-by-step explanation:

ABCD is Rhombus,

$\boxed{\angle ABC + \angle BCD = 180°}$

$\implies 126°+ \angle BCD = 180°$

$\implies \angle BCD = 180° - 126°$

$\implies \boxed{\angle BCD = 54°}$

AC is the diagonal of rhombus ABCD.

We know that, In Rhombus diagonals divide an angle into 2 equal angles.

$\boxed{\angle ACD = \frac{1}{2} \angle BCD}$

$\implies \angle ACD = \frac{1}{2} \times 54°$

$\implies \boxed{ \angle ACD = 27°}$

$\therefore The \: measure \: of \: the \: \underline{\:\bold{\angle ACD \: is \: 27°}\:}.$

More informations:

✵ The sum of two adjacent angles is equal to 180 degrees.

✵ Opposite angles of a rhombus are equal.

✵ All sides of the rhombus are equal.

✵ The opposite sides of a rhombus are parallel.

✵ In a Rhombus, the diagonals are not necessarily equal.