Question

Solve :

8) Two adjacent angles of a parallelogram are in the ratio 1: 2. Find the measures of
all the angles of the parallelogram​

Answer 1

Answer:

Let ABCD be the parallelogram.

The ratio of measures of two adjacent angles of a parallelogram is 1 : 2.

Let the common multiple be x.

∴ ∠A = x° and ∠B = 2x° ∠A + ∠B = 180° [Adjacent angles of a parallelogram are supplementary]

∴ x + 2x = 180

∴ 3x = 180

∴ x = 180/3

∴ x = 60

ii. ∠A = x° = 60°

∠B = 2x° = 2 x 60° = 120°

∠A = ∠C = 60°

∠B = ∠D= 120° [Opposite angles of a parallelogram]

∴ The measures of the angles of the parallelogram are 60° , 120° , 60° and 120°.

Answer 2

Answer:

let the 2 adjacent angles be x and 2x

x+2x =180 - co interior angles

3x =180

x= 60

2x=120

opposite angles of parallelogram are equal

measure of angles of parallelogram are 60 ,120 ,60 ,120

Explanation:

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