Question

What is the measure of

Answer 1

∠ABE = 65. This is an acute angle

∠EBD = 26. This is an acute angle.

∠DBC = 89. This is an acute angle.

Step-by-step 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:

`\begin{gathered} (6x)/(6)=(198)/(6) \\ \\ x\text{ = }33 \end{gathered}`

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.