Respuesta :

[tex]\\ \sf\longmapsto x+2x+90=180[/tex]

[tex]\\ \sf\longmapsto 3x+90=180[/tex]

[tex]\\ \sf\longmapsto 3x=180-90[/tex]

[tex]\\ \sf\longmapsto 3x=90[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{90}{3}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Now

[tex]\\ \sf\longmapsto x=2y[/tex](Opposite interior angles)

[tex]\\ \sf\longmapsto 2y=30[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto y=15[/tex]

And

[tex]\\ \sf\longmapsto x+z=180[/tex]

[tex]\\ \sf\longmapsto z+30=180[/tex]

[tex]\\ \sf\longmapsto z=180-30[/tex]

[tex]\\ \sf\longmapsto z=150[/tex]

mhanifa

Answer:

Figure 1

Straight angle is 180°:

  • 2x + 90° + x = 180° ⇒ 3x = 90° ⇒ x = 30°

Alternate interior angles are congruent:

  • 2y = x ⇒ 2y = 30° ⇒ y = 15°

Consecutive interior angles are supplementary:

  • x + z = 180° ⇒ z = 180° - 30° ⇒ z = 150°

Figure 2

Alternate interior angles:

  • 3x = 5x - 20° ⇒ 2x = 20° ⇒ x = 10°

Sum of interior angles of a triangle:

  • 2y + 4y + 5x - 20 = 180° ⇒ 6y + 5*10° = 200° ⇒ 6y = 150° ⇒ y = 25°

Otras preguntas