Question

adjacent angles of the Rhombus are in the ratio 2:3 find measure of all angles​

Answer 1

Answer:

Rhombus is a special tupe of quadrilateral whose all sides are equal and opposite angles are equal.

Let us consider a rhombus ABCD

here let the angles <B and <C

are in ratio as given above = 2:3

• using tge property of rhombus that opposite angles are equal

We get

• <B= <D
• <C = <A

Let us consider the ratio to be x

So <B= 2x and <C = 3x

Using angle sum property of quadrilateral ie, sum of all angles of a quadrilateral is 360

<A +<B + <C + <D = 360°

• NOW as <A = <C and <B = <D

so putting their values

<A +<B +<A+<B=360

2<A + 2<B = 360

<A + <B = 180°

• As <A = 2x and <B = 3x so putting the values.

2x + 3x = 180

5x = 180

x = 180/5

x = 36°

Now

<A = 2x = 2×36 = 72°

<B = 3x = 3 × 36 = 108°

<C = <A = 72°

<D = < B = 108°