Question

the angles of a quadrilateral are in the ratio 4:7:9:10. what is the sum of the measures of the smallest angle and the largest angle of the quadrilateral?

Answer 1

Answer:

Step-by-step explanation:

angle sum of quadrilateral =360 degree

4x+7x+9x+10x=360

30x=360

x=360/30

=12

smallest angle=4x= 4*12=48

largest angle=10x=10*12=120

48+120=168

Answer 2

Answer :

• The sum of the largest and smallest angle is 168°.

Given :

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

To Find :

• Sum of largest and smallest angle of the quadrilateral.

Solution :

Put x in the ratio

Now, angles are

• 4x

• 7x

• 9x

• 10x

As we know that

• Sum of all angles of a quadrilateral is 360°

Now

→ 4x + 7x + 9x + 10x = 360°

→ 11x + 19x = 360°

→ 30x = 360

→ x = 360/30

→ x = 12

Put the value of x in the ratio

• First angle 4x = 4 × 12 = 48°

• Second angle 7x = 7 × 12 = 84°

• Third angle 9x = 9 × 12 = 108°

• Fourth angle 10x = 10 × 12 = 120°

Here

• Smallest angle = 48°

• Largest angle = 120°

Sum of smallest and largest angle

→ 48° + 120°

→ 168°

Hence, the sum of the largest and smallest angle is 168°.