Question

The mean of three angles of quadrilateral is 64 if the ratio of the angle are 4:5:7. Find the four angles of quadrilateral

Answer 1

Answer:

The four angles of the quadrilateral are 48°, 60°, 84° & 168°.

Step-by-step-explanation:

The ratio of three angles of a quadrilateral is 4 : 5 : 7.

Let the common multiple be x.

∴ The three angles are 4x, 5x & 7x.

We know that,

The sum of measures of angles of a quadrilateral is 360°.

∴ 4x + 5x + 7x + Fourth angle = 360°

⇒ 16x + Fourth angle = 360

⇒ Fourth angle = ( 360 - 16x )°

Now,

The mean of three angles is 64.

∴ ( 4x + 5x + 7x ) / 3 = 64

⇒ 4x + 5x + 7x = 64 * 3

⇒ 16x = 64 * 3

⇒ x = 64 ÷ 16 * 3

⇒ x = 4 * 3

⇒ x = 12

Now,

The angles of the quadrilateral are

4x = 4 * 12 = 48°

5x = 5 * 12 = 60°

7x = 7 * 12 = 84°

( 360 - 16x ) = 360 - 16 * 12 = 360 - 192 = 168°

∴ The four angles of the quadrilateral are 48°, 60°, 84° & 168°.

Answer 2

Given :-

The mean of three angles of quadrilateral is 64 if the ratio of the angle are 4:5:7.

To Find :-

four angles of the quadrilateral

Solution :-

We know that

Sum of all angle of a quadrilateral = 360. The average of three is angle is 64.

(4x + 5x + 7x)/3 = 64

(16x)/3 = 64

16x = 64 × 3

x = 64 × 3/16

x = 4 × 3

x = 12°

Now

4x = 4(12) = 48

5x = 5(12) = 60

7x = 7(12) = 84

Now,

∠A + ∠B + ∠C + ∠D = 360°

48 + 60 + 84 + ∠D = 360°

192 + ∠D = 360°

∠D = 360 - 192

∠D = 168°