What is the possible values of x? The diagram is not to scale. Please show all steps in order to earn full credit.
there in an image showing two triangles connected to each other, the angles of triangle 1 are labeled ABD, and triangle 2 is CDB. angle B, on the side of triangle 1, is 63 degrees. line AD equals 11 units in length. line DC equals 8 units in length. the angle B, on the side of triangle 2, is (8x+7) degrees.
To find the possible values of x, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
In triangle 1, we know that angle ABD = 63 degrees.
In triangle 2, angle CDB = 180 - angle B - angle CDB.
Since angle B = 8x + 7 degrees, we can write:
angle CDB = 180 - (8x + 7) - angle B.
Since triangle 1 and triangle 2 share side BD, angle ABD = angle CDB.
Therefore, 63 = 180 - (8x + 7) - angle B.
Substituting the known values:
63 = 180 - (8x + 7) - 63.
We can simplify this equation:
63 = 180 - 8x - 7 - 63.
63 = 113 - 8x - 63.
63 = 113 - 8x - 63.
63 = 113 - 8x - 63.
8x = 113 - 63.
8x = 50.
x = 50/8.
x = 6.25.
So the possible value of x is 6.25.