Question

find the value of x.
20.
21.
22.
23.
24.

Explanation:

Step1: Use the property of same - side interior angles

For problem 20, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. So \(58+(x + 18)=180\).

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Step2: Use the property of alternate interior angles

For problem 21, when two parallel lines are cut by a transversal, alternate interior angles are equal. So \(2x = 60\).

$$x=\frac{60}{2}=30$$

Step3: Use the property of corresponding angles

For problem 22, when two parallel lines are cut by a transversal, corresponding angles are equal. So \(2x-4 = 92\).

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Step4: Use the property of alternate interior angles

For problem 23, when two parallel lines are cut by a transversal, alternate interior angles are equal. So \(5x-10=75\).

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Step5: Use the property of corresponding angles

For problem 24, first find the adjacent - angle of \(120^{\circ}\), which is \(180 - 120=60^{\circ}\). Then, since the lines are parallel and using the property of corresponding angles, \(3x=60\).

$$x = 20$$

Answer:

1. \(104\)
2. \(30\)
3. \(48\)
4. \(17\)
5. \(20\)