Question

two adjacent angle of a rhombus are in the ratio 2 ratio 4 find all the angles of the Rhombus

Answer 1

Question :- Two adjacent angles of a rhombus are in the ratio 2 : 3. Find all the angles of the rhombus.


Solution :-

Ratio of two adjacent angles of a rhombus is 2 : 3

Let the common multiple be x

So, let the 1st angle be 2x and 2nd angle be 3x

Sum of adjacent angles of a rhombus is 180°


According to the given condition,

2x + 3x = 180

∴ 5x = 180

Dividing both the sides by 5

∴ $\boxed{x = 36}$


∴ 1st angle ➾ 2x

➾ 2 × 36

➾ $\boxed{\boxed{\tt{72^{\circ}}}}$


∴ 2nd angle ➾ 3x

➾ 3 × 36

➾ $\boxed{\boxed{\tt{108^{\circ}}}}$



∴ The angles of the rhombus are 72°, 108°, 72° and 108°

Answer 2

According to the attachment, the ratio is 2:3 , so I am taking that ratio.

$\boxed{ \bf{refer \: to \: attachment \: for \: figure \: }}$

$\underline{\textbf{Given :- }}$ The ratuos of two adjacent angles of rhombus is 2:3 .

$\underline{\textbf{To find :- }}$ all angles of rhombus.

$\underline{\textbf{Solution :-}}$

Let the common ratio be x.

So, the two adjacent angles become 2x and 3x .

We know that rhombus is a parallelogram and in a parallelogram the sum of the adjacent angles is equal to 180° (co - interior angles)

Now, angle A + angle B = 180°

$\implies$2x +3x =180°

$\implies$5x=180°

$\implies$x=$\bf{\frac{180 ^ {\circ}}{5}}$

$\implies$x= 36°

So,

angle A = 2x

=2×36 °

= 72°

Angle B =3x

=3×36°

= 108°

Now, the opposite angles of a parallelogram are equal.

So, $\boxed{\textbf{Angle A = angle C = 72^{circ}}}$

and $\boxed{\textbf{Angle B = angle D = 108^{circ}}}$