Question

a diagonal and side of a rhombus are of equal length find the measure of the angles of the Rhombus

Answer 1

Let the side of the rhombus be 'a' cm.

As diagonal is equal to the side, the sides of triangles formed by the diagonals are a,a,a for both triangles.

So,both are equilateral triangles.

Therefore the angles are 60°,120°,60°,120°.

Answer 2

Answer:

The angles of the given rhombus are found to be:  $60^\circ$ , $120^\circ$ ,  $60^\circ$  and $120^\circ$

Step-by-step explanation:

The rhombus is a parallelogram with opposite sides parallel and its opposite angles equal to each other, but the only specification is a rhombus has all four equal sides.

Thus, if in a rhombus, ABCD, one diagonal let's say BD is equal to the side length, then the triangle formed, ΔABD will be an equilateral triangle.

An equilateral triangle has all three equal sides and each of the three angles of an equilateral triangle is of the measure of $60^\circ$ each.

Thus, ∠A = $60^\circ$.

Now, as the opposite angles of a rhombus are equal so:

∠A = ∠C = $60^\circ$

Now, applying the angle sum property of quadrilateral, we get:

$\angle A+\angle B+\angle C+\angle D=360^\circ$

Putting the values of ∠A and ∠C, we get:

$60^\circ+\angle B+60^\circ+\angle D=360^\circ$

but ∠B = ∠D (opposite angles of rhombus), so:

$120^\circ+\angle B+\angle B=360^\circ$

or we can say:

$2\angle B=360^\circ-120^\circ$

by which we get:

$\angle B=120^\circ$

But as ∠B = ∠D, so:

∠B = ∠D = $120^\circ$

Thus, the angles of rhombus are measured to be:  $60^\circ$ , $120^\circ$ ,  $60^\circ$  and $120^\circ$