Question

the ratio of meaures of two adjecent angles of a parallelogram is 1:2, find measure of all angles of parallelogram .with solution​

Answer 1

let first angle = x

let second angle = 2x

2x+x= 180° ( co-interior angles)

3x=180°

x=60°

first angle=60°

second angle= 120°

third angle = 60°

fourth angle = 120°

Answer 2

Given :-

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

To Find :-

The measures of all angles of parallelogram.

Analysis :-

Consider the common ratio as a variable.

Multiply each angle to the variable. Make an equation accordingly.

Find the value of the variable and find the other angle too.

Solution :-

Consider the common ratio as 'x'. Then the angles would be x and 2x.

We know that,

In parallelogram, sum of adjacent angles = 180°

Making a equation,

x + 2x = 180

3x = 180

By transposing,

x = 180/3

x = 60°

Finding the other angle,

2x = 2 × 60

= 120°

Since they are adjacent angles, the other two sides would be the same too.

Therefore, the angles of the parallelogram are 60°, 120°, 60° and 120°.