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3 years ago

Help im behind my math class. pls

Mathematics

1 answer:

maks197457 [2]3 years ago

7 0

Answer:

Please check the explanation.

Step-by-step explanation:

From the given diagram, we can observe that r and s are the two parallel lines intersected by the two transversal lines.

Therefore, the pairs of alternating interior angles formed by the two transversal lines are:

∠1 & ∠5

∠2 & ∠4

∠2 & ∠7

∠3 & ∠6

We know that alternating interior angles formed by a transversal line are congruent.

Thus,

∠1 = ∠5

∠2 = ∠4

∠2 = ∠7

∠3 = ∠6

Part a)

Given

m∠1 = 3x + 42

m∠5 = 8x - 8

∠1 = ∠5

3x + 42 = 8x - 8

flipe the equation

8x - 8 = 3x + 42

subtract 3x from both sides

8x - 8 - 3x = 3x + 42 - 3x

5x - 8 = 42

add 8 to both sides

5x - 8 + 8 = 42 + 8

5x = 50

divide both sides by 5

5x/5 = 50/5

x = 10.0000 (Rounded to four decimal places)

Thus, the value of x = 10.0000 (Rounded to four decimal places)

Part b)

Given

m∠6 = 12°

It is clear that angles ∠6 and angle ∠7 lie on a straight line.

Thus,

The sum of ∠6 and ∠7 is 180°.

∠6 + ∠7 = 180°

substituting m ∠ 6 = 12° in ∠6 + ∠7 = 180°

12° + ∠7 = 180°

subtract 12 from both sides

12° + ∠7 - 12° = 180° - 12°

∠7 = 168°

Thus, measure of angle ∠7 = 168°.

We already know that alternating interior angles formed by a transversal line are congruent.

∠7 and ∠2 are alternating interior angles.

Thus,

∠2 = ∠7

As ∠7 = 168°.

Therefore,

∠2 = 168°

Hence, we conclude that

∠2 = 168°

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