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Verizon [17]
1 year ago
13

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.

Mathematics
2 answers:
andre [41]1 year ago
8 0

Answer:

\huge\boxed{\sf < 2 = 122\°}

Step-by-step explanation:

From the figure,

<h3>∠1 = ∠2 </h3>
  • (Alternate angles are equal)

<u>We know that:</u>

  • ∠1 = 10x + 2
  • ∠2 = 12x - 22

So,

<h3>10x + 2 = 12x - 22</h3>

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

<h3>x = 12</h3>

Given that,

∠2 = 12x - 22

Put x = 12

∠2 = 12(12) - 22

∠2 = 144 - 22

<h3>∠2 = 122°</h3>

\rule[225]{225}{2}

ss7ja [257]1 year ago
3 0

Answer: 122°

Step-by-step explanation:

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

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°.

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