Respuesta :

[tex]\\ \rm{:}\dashrightarrow p+120=180[/tex]

[tex]\\ \rm{:}\dashrightarrow p=60[/tex]

And

  • q=65°(Opposite angles are equal

Now

[tex]\\ \rm{:}\dashrightarrow r+65=180[/tex]

[tex]\\ \rm{:}\dashrightarrow r=115[/tex]

So

[tex]\\ \rm{:}\dashrightarrow x=q(Opposite interior angles)=65[/tex]

  • y=p=60°
semsee45

Answer:

p = 60°

r = 115°

q = 65°

y = 60°

x = 65°

Step-by-step explanation:

Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.

Therefore, the linear pairs are:

   p + 120° = 180°

⇒ p = 60°

   r + 65° = 180°

⇒ r = 115°

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Vertical angle theorem: a pair of opposite angles formed by intersecting lines.  Vertical angles are always congruent (equal).

Therefore, the vertical angles are q and 65°:

⇒ q = 65°

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Consecutive interior angle theorem:  if a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary and so their measures sum to 180°.

Therefore, the consecutive interiors angles are:

   120° + y = 180°

⇒ y = 60°

   x + r = 180°

⇒ x + 115° = 180°

⇒ x = 65°

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