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: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.