Answer:

1.) To find the value of x, we can use the fact that opposite angles are equal. Therefore, we have:

m∠1 = m∠6

(2x + 20)° = (3x + 30)°

Subtracting 2x from both sides, we get:

20° = x + 30°

Subtracting 30° from both sides, we get:

Answer:

-10° = x

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2.) m∠1 = (2x + 20)°

m∠1 = (2(-10) + 20)°

m∠1 = 0°

ANSWER: m∠1 = 0°

3.) m∠1 + m∠2 = 180°

0° + m∠2 = 180°

m∠2 = 180°

ANSWER: m∠2 = 180°.

4.) m∠3 = m∠6

m∠3 = (3x + 30)°

m∠3 = (3(-10) + 30)°

m∠3 = 0°

ANSWER: m∠3 = 0°.

5.) m∠4 + m∠6 = 180°

m∠4 + (3x + 30)° = 180°

m∠4 + (3(-10) + 30)° = 180°

m∠4 = 120°

ANSWER: m∠4 = 120°.

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