The sum of two angles formed by the intersection of two lines is 114°. find the measures of all angles.

The measures of all angles are 57° , 123° , 57° , 123°

Step-by-step explanation:

* When two lines intersect, they formed 4 angles

- 2 pairs of vertical angles, (opposite angles), and they are congruent

- 4 linear pair of angles that the sum of the measures of each two

   adjacent angles is 180°

- The given is:

  The sum of two angles formed by the intersection of two lines is 114°

∵ The sum of the measures of the two angles is not 180°

∴ The two angles are vertical angles and they are congruent

∵ The two angles are congruent

∵ Their sum is 114°

∴ The measure of each angle = 114 ÷ 2 = 57°

∵ The two line intersected

∴ There are pairs of linear angles are formed

∵ The sum of the measures of a pair of linear angles is 180°

∴ 57° + the measure of the adjacent linear angle = 180°

- Subtract 57 from both sides

∴ The measure of the adjacent linear angle = 123°

* The measures of all angles are 57° , 123° , 57° , 123°

180

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