The adjacent angles of a parallelogram are in the ratio 2:1. Find the measures of all the angles.

Let us assume a parallelogram ABCD,

We know that the sum of the adjacent angles in a parallelogram is 180⁰.

We also know that the angles at the opposite vertices are equal.

i.e., ∠A + ∠B = 180⁰. ...... - (1)

∠A = ∠C ...... ...... (2)

∠B = ∠D ...... ...... (3)

According to the problem, it is given that the adjacent angles are in the ratio of 2:1.

Let us assume that the adjacent angles be A and B.

Let’s take the values of ∠B = 2x and ∠A = x

From eq(1) we get,

⇒ x + 2x = 180⁰

⇒ 3x = 180⁰

⇒

⇒ x = 60⁰.

Now find the value of ∠A and ∠B,

⇒ ∠A = x

⇒ ∠A = 60⁰

⇒ ∠B = 2x

⇒ ∠B = 2 × 60⁰

⇒ ∠B = 120⁰

From (2) and (3) we get,

∠C = 60⁰ and ∠D = 120⁰

The values of ∠A, ∠B, ∠C and ∠D is 60⁰, 120⁰, 60⁰, 120⁰.