Question

In a
quadrilateral A,B,C,D are in ratio 3:5:7:9. Find
the measure of angle D of quadrilateral​

Answer 1

Step-by-step explanation:

The measure of each of these angles is 45,75,105 and 135.

Step-by-step explanation:

Given : The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9.

To find : The measure of each of

these angles ?

Solution:

We know that,

Sum of angle of quadrilateral is 360°.

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

Let x be the common ratio.

$= > 3x + 5x + 7x + 9x = 360$

$= > 24x = 360$

$= > 2x = 30$

$= > x = \frac{ 30}{2}$

$= > 15$

The angle of quadrilaterals are:

$= > 3x = 3 \times 15 = 45$

$= > 5x = 5 \times 15 = 75$

$= > 7x = 7 \times 15 = 105$

$= > 9x = 9 \times 15 = 135$

The measure of each of these angles is 45,75,105 and 135.

Hope it helps you!!

Thank you!!

Answer 2

Question :-

In a quadrilateral A,B,C,D are in ratio 3:5:7:9. Find

the measure of angle D of quadrilateral.

Given :-

Angles A,B,C,D are in ratio 3:5:7:9

To find :-

Measure of Angle D.

Solution :-

Let 'x' be the common ratio

Angle A = 3x

Angle B = 5x

Angle C = 7x

Angle D = 9x

We know that sum of four angles of quadrilateral = 360°

Now,

3x + 5x + 7x + 9x = 360°

24x = 360°

x = 360/24

x = 15

Value of x = 15

Angle A = 3x = 3 × 15 = 45°

Angle B = 5x = 5 × 15 = 75°

Angle C = 7x = 7 × 15 = 105°

Angle D = 9x = 9 × 15 = 135°

Therefore,

Measure of Angle D = 135°