Question

Suppose △ABC has exterior angle at vertex B. The exterior angle is (12x−24)°, m∠A=(3x−6)°, and m∠C=(6x+12)°. What is the measure of the exterior angle at vertex B?
10° degrees


24°24 degrees


96°96 degrees


72°

Answer 1

Answer: 96°

Step-by-step explanation:

If a triangle is being drawn, Angle A and C will be the two remote interior angles in the triangle. The sum of the two interior angles has to equal to the exterior angle.

Set them equal each other and solve for x.

(3x-6) + (6x +12) = 12x - 24     Combine like terms

9x + 6 = 12x - 24          Subtract 6 from both sides

    - 6             -6  

   9x = 12x - 30             Subtract 12x from both sides

-12x       -12x  

    -3x = -30               Divide both sides by -3    

 x = 10      

Now since  x is 10 degrees we will need to input the value into in for x in the exterior angle expression and break it down.  

   Exterior :  12(10) - 24

                    120 - 24  = 96

    This means the measure of the exterior angle at vertex B is  96 degrees.