Question

The angles of a parallelogram are in the ratio of 3:5:9:13 find all the angles of the parllogram

Answer 1

Answer:

Step-by-step explanation:

sum of angles of parallelogram = 360

let the angles be 3x , 5x, 9x and 13x

so  360 = 3x + 5x+ 9x + 13x

360= 30x

360/30 = x

12 = x

thus the angles are

5x = 60 degree

3x = 36 degree

9x = 108 degree

13x = 156 degree

plzzz mark as brainliest if it is right

Answer 2

Given :-

Ratio of the angles = 3 : 5 : 9 : 13

Required to find :-

• Find all the angles of the parallelogram ?

Solution :-

Given information :-

The angles of the parallelogram are in the ratio of 3 : 5 : 9 : 13

we need to find the measurements of all angles of the parallelogram

So,

Let's consider ;

• 1st angle = 3x

• 2nd angle = 5x

• 3rd angle = 9x

• 4th angle = 13x

As we know that ;

In a quadrilateral , sum of all angles is equal to 360°

This implies ,

➜ 3x + 5x + 9x + 13x = 360°

➜ 30x = 360°

➜ x = 360°/30

➜ x = 12°

The value of " x " is 12°

Hence,

The measurements of the angles are ;

• 1st angle = 3x = 3(12°) = 36°

• 2nd angle = 5x = 5(12°) = 60°

• 3rd angle = 9x = 9(12°) = 108°

• 4th angle = 13x = 13(12°) = 156°

Concept used :-

• In a parallelogram, Opposite sides are equal

• Opposite angles are equal

• Sum of two adjacent angles is supplementary

• Diagonals bisect each other

• If a quadrilateral satisfies all these conditions then it is said to a parallelogram