Question

the angles of a quadrilateral are are in the ratio4:7:9:10 what is the sum of the measure of a smallest angle and the largest angle​

Answer 1

Given:-

• The angles of quadrilateral are in ratio of 4:7:9:10.

To find:-

• Sum of measure of a smallest and largest angle.

Solution:-

Let,

First angle be '4x°'.

Second angle be '7x°'.

Third angle be '9x°'.

And Fourth angle be'10x°'.

We know that,

Sum of all angles of quadrilateral is 370°

So,

→ 4x° + 7x° + 9x° + 10x° = 360°

→ 30xπ = 360°

→ x = 360°/30°

→ x = 12

Verification:-

→ 4x° + 7x° + 9x° + 10x° = 360°

• Put x = 12

→ (4×12)° + (7×12)° + (9×12)° + (10×12)° = 360°

→ 48° + 84° + 108° + 120° = 360°

→ 360° = 360°

Hence, verified.

Angles will be

4x = (4×12) = 48°

7x = (7×12) = 84°

9x = (9×12) = 108°

10x = (10×12) = 120°

Smallest angle is 48°

Largest angle is 120°

Sum of largest angle and smallest angle is

→120° + 48°

→ 168°

Sum of largest angle and smallest angle is 168°.

Answer 2

Sum of largest and smallest angle is = 168degree