Question

Please help me ASAP I will mark branlist just explain

Answer 1

Measure of Angle 5 = 150 degree.

Explanation:

Given line g and h are parallel lines.

Let angle measuring
`30\ degree` be a.

From figure we can see that
`\angle a\ and\ \angle 3` both are Linear Pair Postulate,

i.e.
`\angle\ a+\angle 3 =180\ degree`

So,

`30\ degree +\angle 3 =180\ degree`

`\angle 3 = 180-30`

`\Therefore \angle 3=150\ degree` ------------(equation 1)

Now,
`\angle\ a\ and\ \angle\ 4` are alternate interior angles, and alternate interior angles are equal.

i.e.
`\angle\ a = \angle 4`

Therefore
`\angle\ 4 =30\ degree` ------------(equation 2)

Now,
`\angle 4\ and\ \angle 7` both are Linear Pair Postulate,

i.e.
`\angle\ 4 +\angle\ 7 = 180\ degree`

`30+\angle\ 7=180` ------------------(from equation 2)

`\angle\ 7 =180-30`

`\therefore\ \angle\ 7 = 150\ degree` ---------(equation 3)

Now,
`\angle\ 7\ and \angle\ 5` are vertically opposite angles, and vertically opposite angles are equal.

So,

`\angle 7=\angle 5`

`\therefore\ \angle 5=150\ \ degree` -----------------(from equation 3)