Question

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

Answer 1

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°

Answer 2

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

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

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

`\\ \sf\longmapsto 3x=90`

`\\ \sf\longmapsto x=(90)/(3)`

`\\ \sf\longmapsto x=30`

Now

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

`\\ \sf\longmapsto 2y=30`

`\\ \sf\longmapsto y=(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`