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Two lines and a ray intersect to form five angles. The angles are numbered in the diagram 1 through 5.
If the measure of ∠4 is 55°, what is the measure of ∠2?

Respuesta :

MrRoyal

Answer:

[tex]\angle 2 =145^\circ[/tex]

Step-by-step explanation:

Given

[tex]\angle 4 = 55^\circ[/tex]

Required

Find [tex]\angle 2[/tex]

From the attached image, we have:

[tex]\angle 5 = 90[/tex] --- right angle

So, we have:

[tex]\angle 5 +\angle 4 = 90 + \angle 4[/tex]

Substitute: [tex]\angle 4 = 55^\circ[/tex]

[tex]\angle 5 +\angle 4 = 90 + 55[/tex]

[tex]\angle 5 +\angle 4 = 145[/tex]

To solve for [tex]\angle 2[/tex], we have:

[tex]\angle 2 =\angle 5 +\angle 4[/tex] --- Vertically opposite angles

So:

[tex]\angle 2 =145^\circ[/tex]

Ver imagen MrRoyal