Question

find the sum of x + y + z in the following figures​

Answer 1

Answer:

x + y + z = 360°

Step-by-step explanation:

X:

If you observe the figure, x and 52° are adjacent to each other.

So,

x + 52° = 180° [Sum of adjacent angles = 180°]

x = 180° - 52°

x = 128°

Z:

If you observe the figure, z and 49° are adjacent to each other as well.

z + 49° = 180° [Sum of adjacent angles = 180°]

z = 180° - 49°

z = 131°

Y:

Before finding out the value of y, we should first find out the value of the 3rd unknown angle of the triangle.

Let the 3rd unknown angle be 'a'.

49° + 52° + a = 180° [Sum of the 3 vertex angles of a triangle = 180°]

101° + a = 180°

a = 180° - 101°

a = 79°

Now, we can find out the value of y.

If you observe again, y and a are adjacent to each other.

y + a = 180°[Sum of adjacent angles = 180°]

y + 79° = 180°

y = 180° - 79

y = 101°

Now, we can find out the sum of x, y, and z.

x + y + z

⇒ 128° + 101° + 131°

⇒ 360°