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Step-by-step explanation:

1) Vertically opposite angles are equal.

x + 30 = 180 - 2x

Add '2x' to both sides

x + 30  +2x = 180

3x + 30 = 180

Subtract 30 from both sides

3x = 180 - 30

3x = 150

 x = 150/3

x = 50

2)  Let the angle be x

It's complement angle = 90 - x

The angles are : 36 , 54

3) Let the angle be x

It's supplement = 180 - x

Angles are  30 , 150

4) Ratio = 7 : 3

The angles are = 7x , 3x

7x + 3x = 180

10x = 180

x = 180/10

x = 18

7x = 7 * 18 = 126

3x = 3 * 18 = 54

Angles are 126 , 54

1. Intersecting lines are lines that cross each other. When two lines intersect, the opposite angles are equal.

Given: x + 30° and 180° - 2x are vertically opposite angles

⇒   x + 30° = 180° - 2x

⇒   3x = 150°

⇒   x = 50°

2. Let the complement be : C

Given : The other angle is two third of its complement

Two angles are said to be Complementary if their sum is equal to 90°

The size of the angle which is two third of its complement is 36°

3. Let the supplement be : S

Given : The other angle is one fifth of its supplement

Two angles are said to be Supplementary if their sum is equal to 180°

The size of the angle which is one fifth of its supplement is 30°

4. Two supplementary angles are in the ratio 7 : 3

Let the supplementary angles be : 7S and 3S

Two angles are said to be Supplementary if their sum is equal to 180°

⇒   7S + 3S = 180°

⇒  10S = 180°

⇒   S = 18°

First Angle : 7S = (7 × 18) = 126°

Second Angle : 3S = (3 × 18) = 54°