Respuesta :

Answer:

m∠ABE = 45°

Step-by-step explanation:

∠ABD is a straight angle then it measures m∠ABD = 180°

On the other hand , m∠ABD = m∠DBC + m∠CBE + m∠ABE

Therefore, (we get this equation)

m∠DBC + m∠CBE + m∠ABE = 180°

Solving the equation:

m∠ABE = 180 - (m∠DBC + m∠CBE)

              = 180 - (115 + 20)

              = 180 - 135

              = 45°

If ∠ABD is a straight line, then the sum of the measures of ∠ABE, ∠EBC, and ∠CBD should be equivalent to 180°. Therefore,

[tex]\implies \angle ABE + \angle EBC + \angle CBD = 180\°[/tex]

We are given the following measures:

  • [tex]\angle EBC = 20\°[/tex]
  • [tex]\angle CBD = 115\°[/tex]

Now, plug the measures into the equation [∠ABE + ∠EBC + ∠CBD = 180°]

[tex]\implies \angle ABE + \angle EBC + \angle CBD = 180\°[/tex]

[tex]\implies \angle ABE + 20 + 115 = 180[/tex]

Now, simplify by adding:

[tex]\implies \angle ABE + 20 + 115 = 180[/tex]

[tex]\implies \angle ABE + 135 = 180[/tex]

Furthermore, to determine the measure of ∠ABE, isolate it on one side of the equation. This can be done by subtracting 135 on both sides.

[tex]\implies \angle ABE + 135 - 135 = 180 - 135[/tex]

[tex]\implies \boxed{\angle ABE = 45\°}[/tex]

Otras preguntas