Question

Given: Angle 2 is 65 degrees. What is the angle measurement of Angle 4. Explain the angle relationship used and show your work. What is the angle measurement of Angle 7. Explain the angle relationship used and show your work. What is the angle measurement of Angle 3. Explain the angle relationship used and show your work.

Answer 1

`\angle 4 = 115^(\circ)`

`\angle 3 = 65^(\circ)`

`\angle 7 = 65^(\circ)`

Explanation:

Given

`\angle 2 = 65^(\circ)`

See attachment

Solving (a):
`\angle 4`

To solve for
`\angle 4`, we make use of:

`\angle 2 +\angle 4 = 180^(\circ)`

The relationship between both angles is that they are complementary angles

Make
`\angle 4` the subject

`\angle 4 = 180^(\circ) - \angle 2`

Substitute
`65^(\circ)` for
`\angle 2`

`\angle 4 = 180^(\circ) - 65^(\circ)`

`\angle 4 = 115^(\circ)`

Solving (b):
`\angle 3`

To solve for
`\angle 3`, we make use of:

`\angle 3 =\angle 2`

The relationship between both angles is that they are complementary angles

`\angle 3 = 65^(\circ)`

Solving (c):
`\angle 7`

To solve for
`\angle 7`, we make use of:

`\angle 7 = \angle 3`

The relationship between both angles is that they are alternate exterior angles.

So:

`\angle 7 = 65^(\circ)`