Question

Four angles of a quadrilateral are in the ratio 7:8:10:11. Find their measures.

Answer 1

Answer:

The measures of the angles of the quadrilateral are 70°, 80°, 100° and 110°.

Step-by-step-explanation:

The angles of a quadrilateral are in the ratio 7 : 8 : 10 : 11.

Let the common multiple be x.

∴ The angles of the quadrilateral become 7x, 8x, 10x and 11x.

We know that,

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

∴ 7x + 8x + 10x + 11x = 360

⇒ 15x + 10x + 10x + x = 360

⇒ 15x + x + 20x = 360

⇒ 16x + 20x = 360

⇒ 4x + 5x = 90 - - - - - [ Dividing by 4 ]

⇒ 9x = 90

⇒ x = 90 ÷ 9

⇒ x = 10°

Now,

First angle = 7x = 7 * 10

∴ First angle = 70°

Second angle = 8x = 8 * 10

∴ Second angle = 80°

Third angle = 10x = 10 * 10

∴ Third angle = 100°

And,

Fourth angle = 11x = 11 * 10

∴ Fourth angle = 110°

∴ The measures of the angles of the quadrilateral are 70°, 80°, 100° and 110°.

Answer 2

Answer:

"

$\tt \red{angles = } \\ \huge \tt \red{70°, 80°, 100°, 110°}$

Step-by-step explanation:

Given -

four angles of a quadrilateral are in ratio = 7 : 8 : 10 : 11

.

To find -

All four angles

.

Solution -

Let the four angles are 7x, 8x, 10x and 11x respectively

.

We know that,

sum of all four angles of quadrilateral = 360°

=> 7x + 8x + 10x + 11x = 360°

=> 36x = 360°

=> x = 360/36

=> x = 10°

.

Now,

first angle = 7x = 7×10° = 70°

second angle = 8x = 8×10° = 80°

third angle = 10x = 10×10° = 100°

fourth angle = 11x = 11×10° = 110°

.

Sum of all angles is 360°, and ratio of angles is 7:8:10:11. So we are sure that our answer is correct.

hope it helps.