Question

the angle of a quadrilateral are in the ratio 3:5:7:9. find the measureof these angle​

Answer 1

$\huge\underline\bold{QUESTION:-}$

___________________________________________

The angles of a quadrilateral are in the ratio 3:5:7:9. Find the measure of each angle

___________________________________________

$\large\underline\bold{TO FIND:-}$

___________________________________________

The measure of each angle if the angles are in the ratio 3:5:7:9

___________________________________________

$\large\underline\bold{SOLUTION:-}$

$\rightarrow$ The ratios of angle= 3:5:7:9

$\rightarrow$ The sum is all angles in a quadrilateral= 360°

$\rightarrow$ Use, Sum of terms of ratio

Sum of terms of ratio : Ratios of angles= 3:5:7:9

Sum of terms of ratio= 3+5+7+9

Sum of ratios= 24

$\rightarrow$ Each ratio × 360 / Sum of ratios

1st angle= 3 × 360 / 24= 45°

2nd angle= 5 × 360 / 24= 75°

3rd angle= 7 × 360 / 24= 105°

4th angle= 9 × 360 / 24= 135°

$\large\underline\bold{VERIFICATION:-}$

______________________________________

$\rightarrow$ Sum of all the angles of a quadrilateral= 360°

Then, 45°+75°+105°+135°= 360°

So, 360°= 360°

Answer 2

═════════════

☞ Given :-

• The angle of a quadrilateral are in the ratio 3:5:7:9.

☞ To Find :-

• The measure of all angles.

☞ Solution :-

Let the number be x.

So, The Angles Are :-

3x, 5x, 7x, 9x.

Sum Of All the Angles Of A Quadrilateral = 360°

So, The Equation :-

3x + 5x + 7x + 9x = 360°

➨ 24x = 360°

➨ x = 360/24

➨ x = 15°

So, 3x = 45°, 5x = 75°, 7x = 105°, 9x = 135°.

Hence, The Angles are 45°, 75°, 105°, 135° respectively.

═════════════