In a rhombus ABCD, AC=AB. State the measure of ∠D and ∠BAD respectively. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Let the figure be -

Given:

AC = AB

As we know, all sides and diagonals of a rhombus is equal -
So,

AB = BC = CD = DA = AC

Here,

AC

is diagonal of rhombus,
Now,
In

ΔACD

and

ΔABC

is equilateral

Δ

because here all sides are equal.
So, in

ΔACD

AC = CD = DA

∴ Each angle of equilateral

Δ

60 °

As we know, rhombus is also parallelogram and sum of adjacent angles of parallelogram is

180 °

∠ D + ∠ A = 180 °

60 ° + ∠ A = 180 °

∠ A = 180 ° - 60 °

∠ A = 120 °

∠ BAD = 120 °

In a rhombus $ABCD, AC = AB$ . State the measure of $∠ D$ and $∠ BAD$ respectively.