Question

Two lines and a ray intersect to form five angles. The angles are numbered in the diagram 1 through 5.

Answer 1

Answer:

$\angle 2 =145^\circ$

Step-by-step explanation:

Given

$\angle 4 = 55^\circ$

Required

Find $\angle 2$

From the attached image, we have:

$\angle 5 = 90$ --- right angle

So, we have:

$\angle 5 +\angle 4 = 90 + \angle 4$

Substitute: $\angle 4 = 55^\circ$

$\angle 5 +\angle 4 = 90 + 55$

$\angle 5 +\angle 4 = 145$

To solve for $\angle 2$, we have:

$\angle 2 =\angle 5 +\angle 4$ --- Vertically opposite angles

So:

$\angle 2 =145^\circ$