Question

If you know the measure of one of the 8 angles, you can find the measure of all of the others. Try it. The measure of <1 = 120 degrees

Answer 1

`\angle 2 =60`

`\angle 3 = 60`

`\angle 4 = 120`

`\angle 5 = 120`

`\angle 6 = 60`

`\angle 7 = 60`

`\angle 8 = 120`

Explanation:

Given

`\angle 1 = 120^\circ`

See attachment

Required

Determine the other angles

`\angle 1` and
`\angle 2` are on a straight line.

So;

`\angle 1 + \angle 2 =180`

Make
`\angle 2` the subject

`\angle 2 =180 - \angle 1`

`\angle 2 =180 - 120`

`\angle 2 =60`

`\angle 1` ,
`\angle 4`,
`\angle 5` and
`\angle 8` are corresponding angles.

So;

`\angle 4 =\angle 1 = 120`

`\angle 5 =\angle 1 = 120`

`\angle 8 =\angle 1 = 120`

Similarly;
`\angle 2` ,
`\angle 3`,
`\angle 6` and
`\angle 7` are corresponding angles.

So;

`\angle 3 =\angle 2 = 60`

`\angle 6 =\angle 2 = 60`

`\angle 7 =\angle 2 = 60`