Question

A triangle with exterior angles is shown. A triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2 h) degrees. The top interior angle of the triangle is 40 degrees. What is the value of h? h = 20 h = 35 h = 55 h = 70

Answer 1

option 3

Explanation:

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Answer 2

Option 3.

Explanation:

It is given that a triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2h) degrees.

The top interior angle of the triangle is 40 degrees.

`\angle BAC=40`

From the given figure it is clear that

`\angle ABC+2h=180` (Supplementary angle)

`\angle ABC=180-2h`

`\angle ACB+2h=180` (Supplementary angle)

`\angle ACB=180-2h`

According to the angle sum property of triangle, the sum of all interior angles of a triangle is 180 degree.

`\angle ABC+\angle ACB+\angle BAC=180`

`(180-2h)+(180-2h)+40=180`

Combine like terms.

`(180+180+40)+(-2h-2h)=180`

`400-4h=180`

`-4h=180-400`

`-4h=-220`

Divide both sides by -4.

`h=(-220)/(-4)`

`h=55`

The value of h is 55.

Therefore, the correct option is 3.