Question

Please help me ASAP I will mark branlist just explain

Answer 1

Answer:

Measure of Angle 5 = 150 degree.

Step-by-step 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)