Question

pqrs is a rhombus with angle qps 50 find angle rqs

Answer 1

Answer:

∠ rqs = 65°

Step-by-step explanation:

Given : pqrs a rhombus

           ∠ qps = 50°

          ∠ rqs = ?

Solution : In rhombus opposite angles are equal,

                so ∠ qps = ∠ qrs = 50°

Consider Δ qrs, ∠ qrs + ∠ rsq + ∠ rqs = 180°  ----1  ∵ angle sum property

                  In rhombus all sides are equal, qr = rs

                  ∴     ∠ rsq =    ∠ rqs -----------2

Substituting 2 in 1 we get

 ∠ qrs + ∠ rsq + ∠ rqs = 180°

∠ qrs + ∠ rqs + ∠ rqs = 180°

        2 ∠ rqs = 180 - ∠ qrs

                     = 180-50

                     = 130

           ∠ rqs = 130/2

                    = 65°

                 

         

         

Answer 2

Given:

• PQRS is a rhombus
• ∠QPS = 50°

To Find:

• The value of the angle RQS.

Solution:

We know that in a rhombus opposite angles are equal.

∴ ∠QPS = ∠QRS = 50°

Consider ΔQRS,

∠QRS+∠RSQ+∠RQS = 180° →(equation 1) ( Angle sum property of a triangle )

Let 'x' be the values of ∠RQS.

In a rhombus all the sides are equal.

∴ x = ∠RSQ = ∠RQS

Hence equation 1 becomes,

⇒ 50°+x+x = 180°

⇒ 50°+2x = 180°

⇒ 2x = 180°-50°

⇒ 2x = 130°

⇒ x = 130°/2

⇒ x = 65°

⇒ ∠RQS = 65°

∴ The value of the angle RQS = 65°