Question

if angles of a triangle are in the ratio 2:4:9, then the difference of the two smaller exterior angles of the triangle is:

Answer 1

Define x:

Ratio of the angles = 2 : 4 : 9

Let x be the constant ratio

Ratio of the angles = 2x : 4x : 9x

Solve x:

Sum of angles in a triangle = 180º

2x + 4x + 9x = 180

15x = 180

x = 12

Find the angles:

2x = 2 (12) = 24º

4x = 4(12) = 48º

9x = 9(12) = 108º

Find the exterior angles:

interior angle + exterior angle = 180º

Interior angle = 24º, exterior angle = 180 - 24 = 156º

Interior angle = 48º, exterior angle = 180 - 48 = 132º

Interior angle = 108º, exterior angle = 180 - 108 = 72º

Find the difference of the two smaller exterior angles:

Difference = 132 - 72  = 60º

Answer: 60º

Answer 2

Your answer is in the attachment