To find the value of x, we can use the fact that the sum of angles around a point is 360°.
Since ∠ABD = 112°, we can calculate the value of x by using the equation:
∠ABD + ∠DBC + ∠CBD + ∠ABE + ∠EBC = 360°
112° + 2x + x + (5x - 20) + (3x - 10) = 360°
112° + 2x + x + 5x - 20 + 3x - 10 = 360°
11x + 82 = 360°
11x = 278°
x = 25.27
Therefore, the value of x is 25.27. None of the given options match this exact value, but the closest one is x = 20.
If the measure of ∠ABD is 112°, determine the value of x.
x = 5
x = 20
x = 45
x = 67
x = 100
3 answers
here is the options (3x + 7) degrees and (2x + 5) degrees
Let's calculate the value of x using the given options:
∠ABD = 112°
∠DBE = (3x + 7)°
∠EBC = (2x + 5)°
Since the sum of angles around a point is 360°:
112 + 3x + 7 + 2x + 5 = 360
112 + 5x + 12 = 360
5x + 124 = 360
5x = 236
x = 47.2
Therefore, the value of x is 47.2 degrees.
∠ABD = 112°
∠DBE = (3x + 7)°
∠EBC = (2x + 5)°
Since the sum of angles around a point is 360°:
112 + 3x + 7 + 2x + 5 = 360
112 + 5x + 12 = 360
5x + 124 = 360
5x = 236
x = 47.2
Therefore, the value of x is 47.2 degrees.