Question

find the value of x.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: For problem 1

The sum of angles on a straight line is \(180^{\circ}\). So, \(101+(x + 51)=180\).

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Step2: For problem 2

The sum of angles around a point on a straight - line (semicircle) is \(180^{\circ}\). So, \(72+75+(x - 7)=180\).

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Step3: For problem 3

Vertical angles are equal. So, \(4x = 40\).

$$x=\frac{40}{4}=10$$

Step4: For problem 4

The sum of angles on a straight line is \(180^{\circ}\). So, \((x - 72)+118=180\).

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Step5: For problem 5

The sum of angles around a point is \(360^{\circ}\). But considering the right - angle (\(90^{\circ}\)) and the given angles, \(x + 70+164+90=360\).

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Step6: For problem 6

Vertical angles are equal. So, \(5x=25\).

$$x = 5$$

Step7: For problem 7

Vertical angles are equal. So, \(x + 13=56\).

$$x=56 - 13=43$$

Step8: For problem 8

Vertical angles are equal. So, \(x-82 + 133=180\) (sum of angles on a straight line).

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Answer:

1. \(x = 28\)
2. \(x = 40\)
3. \(x = 10\)
4. \(x = 134\)
5. \(x = 36\)
6. \(x = 5\)
7. \(x = 43\)
8. \(x = 129\)