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The sum of two angles formed by the intersection of two lines is 50°. Find the measures of the angles.

please help!!!!! I will award brainliest!!!!!

Respuesta :

anonymous12345678901
When two lines intersect, it creates four angles, 2 of which are equal, and the other 2 are equal due to vertically opposite angles being equal.

Since angles on a straight line equals 180, the two angles we are trying to figure out must be vertically opposite

So to find the measure of the angles simply divide by 2, which will give you the answer 25

The two angles are each 25°
akposevictor

The four angles formed are:

[tex]25^{\circ}, 25^{\circ}, 155^{\circ}, $ and 155^{\circ}.[/tex]

  • When two straight lines intersect, four angles are formed ([tex]\angle A,$ \angle B, $ \angle C, $ and \angle D[/tex]) , while two pairs of vertical angles are formed ([tex]\angle A $ and \angle C; \angle B $ and \angle D[/tex]).

  • Let,

[tex]m \angle A + m \angle C = 50 ^{\circ}[/tex]

  • Therefore:

[tex]m \angle A = \angle C = 25^{\circ}[/tex] (vertical angles are equal)

  • Thus,

[tex]m \angle A = 25^{\circ}\\m \angle C = 25^{\circ}[/tex]

  • Let's find the measures of angles B and D.

[tex]m \angle A + m\angle B = 180^{\circ}[/tex] (angles on a straight line are supplementary)

  • Therefore:

[tex]25 + m\angle B = 180\\m \angle B = 180 - 25\\m \angle B = 155^{\circ}[/tex]

  • Thus:

[tex]m \angle B = m \angle D[/tex] (vertical angles)

[tex]m \angle D = 155^{\circ}[/tex]

Therefore, the measures of the angles are:

[tex]25^{\circ}, 25^{\circ}, 155^{\circ}, $ and 155^{\circ}.[/tex]

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https://brainly.in/question/26526175

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