Question

find the measures of the unknown angles x, y and z​

Answer 1

Answer:

∠x = 80°

∠y = 30°

∠z = 150°

Step-by-step explanation:

∠y = 30° [Vertically Opposite Angles are always equal.]

Now,

∠y + ∠z = 180° [Sum of all angles on a straight line always equals 180°.]

30° + ∠z = 180° [We found out the value of ∠y above.]

∴ ∠z = 180° - 30°

  ∠z = 150°

Now,

∠x + ∠y + 70° = 180° [Sum of all angles on a straight line always

                                  equals 180°.]

∠x + 30° + 70° = 180°

∠x + 100° = 180°

∴ ∠x = 180° - 100°

∠x = 80°

Answer 2

Answer:

x°= 80°, y = 30°, z = 150°

Step-by-step explanation:

There are many ways to find the answers I am showing the simplest ones.

Straight angle: If any three angles add up to 180°(straight line) , they form a straight angle.

Finding x:-

x° + 70° + 30° = 180° (straight angle)

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

Finding y:- ( if u see the image, we observe that ∠x(80), ∠y, ∠70 form straight angle)

y° + x° + 70° = 180°

y° + 80° + 70° = 180°

y° + 150° = 180°

y° = `180° - 150°

y° = 30°

Finding z:- [ After observing the figure, we observe that ∠z and ∠30 form a linear pair ] [ You can also take y°(30) + z° = 180° ]

Linear Pair: If two angles add upto 108° they are said to form linear pair.

z° + 30° = 180°

z° = 180° - 30°

z° = 150°

                Hope it is helpful. Take care.