Answer:
Option 3.
Step-by-step 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.
[tex]\angle BAC=40[/tex]
From the given figure it is clear that
[tex]\angle ABC+2h=180[/tex] (Supplementary angle)
[tex]\angle ABC=180-2h[/tex]
[tex]\angle ACB+2h=180[/tex] (Supplementary angle)
[tex]\angle ACB=180-2h[/tex]
According to the angle sum property of triangle, the sum of all interior angles of a triangle is 180 degree.
[tex]\angle ABC+\angle ACB+\angle BAC=180[/tex]
[tex](180-2h)+(180-2h)+40=180[/tex]
Combine like terms.
[tex](180+180+40)+(-2h-2h)=180[/tex]
[tex]400-4h=180[/tex]
[tex]-4h=180-400[/tex]
[tex]-4h=-220[/tex]
Divide both sides by -4.
[tex]h=\frac{-220}{-4}[/tex]
[tex]h=55[/tex]
The value of h is 55.
Therefore, the correct option is 3.
