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RUDIKE [14]
2 years ago
10

1.Find x,y and z in the figure. 2. find the x and y in the figure ​

Mathematics
2 answers:
STALIN [3.7K]2 years ago
6 0

\\ \sf\longmapsto x+2x+90=180

\\ \sf\longmapsto 3x+90=180

\\ \sf\longmapsto 3x=180-90

\\ \sf\longmapsto 3x=90

\\ \sf\longmapsto x=\dfrac{90}{3}

\\ \sf\longmapsto x=30

Now

\\ \sf\longmapsto x=2y(Opposite interior angles)

\\ \sf\longmapsto 2y=30

\\ \sf\longmapsto y=\dfrac{30}{2}

\\ \sf\longmapsto y=15

And

\\ \sf\longmapsto x+z=180

\\ \sf\longmapsto z+30=180

\\ \sf\longmapsto z=180-30

\\ \sf\longmapsto z=150

melamori03 [73]2 years ago
3 0

Answer:

<h3>Figure 1</h3>

<u>Straight angle is 180°:</u>

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

<u>Alternate interior angles are congruent:</u>

  • 2y = x ⇒ 2y = 30° ⇒ y = 15°

<u>Consecutive interior angles are supplementary:</u>

  • x + z = 180° ⇒ z = 180° - 30° ⇒ z = 150°
<h3>Figure 2</h3>

<u>Alternate interior angles:</u>

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

<u>Sum of interior angles of a triangle:</u>

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