Question

PLEASE HELP WILL GIVE YOU ALL MY POINTS In the picture, t || s, mz1 = 10x + 2, and mz2 = 12x - 22. Find the measure of angle 2.

Answer 1

Answer: 122°

Explanation:

∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.

Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.

`10x+2=12x-22`

`-2x=-24`

`x=12`

Putting x in the expression 12x-22, we get

`12(12)-22\\144-22\\122`

Hence, the value of ∠2 is 122°.

Answer 2

`\huge\boxed{\sf < 2 = 122\°}`

Explanation:

From the figure,

∠1 = ∠2

• (Alternate angles are equal)

We know that:

• ∠1 = 10x + 2
• ∠2 = 12x - 22

So,

10x + 2 = 12x - 22

Add 22 to both sides

10x + 2 + 22 = 12x

10x + 24 = 12x

Subtract 10x to both sides

24 = 12x - 10x

24 = 2x

Divide 2 to both sides

12 = x

OR

x = 12

Given that,

∠2 = 12x - 22

Put x = 12

∠2 = 12(12) - 22

∠2 = 144 - 22

∠2 = 122°

`\rule[225]{225}{2}`