Question

The measure of the exterior angle of the triangle is ___

Answer 1

We know sum of two interior angles=exterior angle

`\\ \sf\longmapsto 2x+18+24=3x+6`

`\\ \sf\longmapsto 2x+42=3x+6`

`\\ \sf\longmapsto 2x-3x=6-42`

`\\ \sf\longmapsto -x=-36`

`\\ \sf\longmapsto x=36`

Exterior angle

`\\ \sf\longmapsto 3x+6`

`\\ \sf\longmapsto 3(36)+6`

`\\ \sf\longmapsto 108+6`

`\\ \sf\longmapsto 114°`

Answer 2

Answer: 114°

Explanation:

Concept:

Here, we need to know the idea of the "Exterior Angle theorem".

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.

If you are still confused, then refer to the attachment below for a graphical explanation.

Solve:

Given

24 + (2x + 18) = 3x + 6

Put like terms together

24 + 18 + 2x = 3x + 6

Combine like terms

42 + 2x = 3x + 6

Subtract 6 on both sides

42 + 2x - 6 = 3x + 6 - 6

36 + 2x = 3x

Subtract 2x on both sides

36 + 2x - 2x = 3x - 2x

x = 36

Exterior angle = 3x + 6 = 3(36) + 6 = 114°

Hope this helps!! :)

Please let me know if you have any questions