ANSWER:
∠ABE = 65. This is an acute angle
∠EBD = 26. This is an acute angle.
∠DBC = 89. This is an acute angle.
EXPLANATION:
Given:
∠ABE = 2x -1
∠EBD = x - 7
∠DBC = 3x - 10
We know total angles on a straight line = 180 degrees
Therefore:
∠ABE + ∠EBD + ∠DBC = 180
2x -1 + x-7 + 3x-10 = 180
Let's solve for x.
Collect like terms:
2x + x + 3x - 10 - 7 - 1 = 180
6x - 18 = 180
Add 18 to both sides:
6x - 18 + 18 = 180 + 18
6x = 198
Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{198}{6} \\ \\ x\text{ = }33 \end{gathered}[/tex]
Substitute x for 33 in the equations above:
∠ABE = 2x -1 = 2(33) - 1 = 66 -1 = 65. This is an acute angle
∠EBD = x - 7 = 33 - 7 = 26. This is an acute angle.
∠DBC = 3x - 10 = 3(33) - 10 = 89. This is an acute angle.
