Answer:

Please FOLLOW, HEART and RATE 5 STARS on my answer. If I help you a lot with this THANK YOU PO.

Step-by-step explanation:

Certainly! Let's solve these geometry problems step by step:

1. Given that "a | | b," we can assume that lines a and b are parallel. When two lines are parallel, the alternate interior angles are congruent. In this case, angles 2 and 3 are alternate interior angles.

We have:

m<2 = 5x - 5

m<3 = 2x + 85

Since angles 2 and 3 are congruent, we can set up an equation:

5x - 5 = 2x + 85

Now, let's solve for x:

5x - 2x = 85 + 5

3x = 90

x = 30

Therefore, x = 30.

2. Given that "m<4 = 3x + 40" and "m<6 = 5x + 12," we can determine the value of x by setting these angles equal to each other. Angle 4 and angle 6 are corresponding angles.

We have:

m<4 = 3x + 40

m<6 = 5x + 12

Since angles 4 and 6 are congruent, we can set up an equation:

3x + 40 = 5x + 12

Now, let's solve for x:

3x - 5x = 12 - 40

-2x = -28

x = 14

Therefore, x = 14.

I hope this helps! Let me know if you have any further questions.