Question

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?

Answer 1

`\angle 2 =145^\circ`

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`