Mathematics, 25.11.2021 15:00 Brainlyisuseful

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Answer from: clairajogriggsk

1) x = 55°

2) x = 30°

3) x = 68°

Step-by-step explanation:

In the given set of questions where it requires to find the unknown value of x to prove that v ||w:

Definition of Consecutive Interior Angles Theorem:

The Consecutive Interior Angles Theorem states that for any given two parallel lines cut by a transversal, the measures of a pair of consecutive interior angles have a sum of 180°. Hence, the pair of consecutive interior angles are supplementary.

Question 1

1.) In the given diagram, the two consective interior angles are m ∠70° and m ∠ 2x°. As defined by the Consecutive Interior Angles Theorem:

m ∠70° + m ∠ 2x° = 180°

Solve for x algebraically:

70° + 2x° = 180°

Subtract 70° from both sides:

70° - 70° + 2x° = 180° - 70°

2x° = 110°

Divide both sides by 2 to solve for x:

$\LARGE\mathsf{\frac {2x^{\circ}}{2}\:=\:\frac{110^{\circ}}{2}}$

x = 55°

Verify whether the value for x is valid:

70° + 2x° = 180°

70° + 2(55)° = 180°

70° + 110° = 180°

180° = 180° (True statement).

Question 2:

2) In the given diagram, the two consective interior angles are m ∠2x° and m ∠ 4x°. As defined by the Consecutive Interior Angles Theorem:

m ∠2x° + m ∠ 4x° = 180°

Solve for x algebraically:

2x° + 4x° = 180°

Add like terms:

6x° = 180°

Divide both sides by 6 to solve for x:

$\LARGE\mathsf{\frac {6x^{\circ}}{6}\:=\:\frac{180^{\circ}}{6}}$

x = 30°

Question 3:

The Consecutive Interior Angles Theorem still applies in this question. The two consective interior angles are m ∠90° and m ∠ (x + 22)°. As defined by the Consecutive Interior Angles Theorem:

m ∠90° + m ∠ (x + 22)° = 180°

Solve for x algebraically:

90° + x° + 22 = 180°

Combine like terms:

112° + x° = 180°

Subtract 112° from both sides to isolate x:

112° - 112° + x° = 180° - 112°

x = 68°

Verify whether the value for x is valid:

90° + x° + 22 = 180°

90° + 68° + 22 = 180°

180° = 180° (True statement).

Answer from: Quest

I'll say voice is the strongest because it give you your personal opinion on things,and your voicing your reasoning..hope that ,if not let me know what i can do :

Answer from: Quest

answer: 2 and 1

step-by-step explanation: got this question

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