Question

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Answer 1

The correct option is (C) x = 78, y = 64 and z =102

Explanation:

Looking into the figure the bigger triangle is having angles 59 and 43, If we add 43 and 14 we get 57. Now we have two angles 57 and 43. We know that triangle angles sum up to 180 so 180 = 59 +(14+43) is the third angle which will become angle 64 which is angle y.

Now look the triangle which is having angles as 14,z,y we already know two angles so we can find third.

14+ 64 + z = 180

z = 102

Similarly in order to find x we take the triangle with angles 59, 43 and x.

59 + 43 + x = 180

x = 78

Answer 2

x = 78

y =64

z=102

Explanation:

The three angles of a triangle add to 180 degrees

59+43+x = 180

102 +x = 180

Subtract 102 from each side

102-102+x = 180-102

x = 78

X and z form a straight line so they add to 180

x+z = 180

78+z =180

Subtract 78 from each side

78-78+z = 180-78

z = 102

The three angles of a triangle add to 180

14+z+y = 180

14+102+y =180

Combine like terms

116+y = 180

Subtract 116 from each side

116-116 +y = 180 -116

y = 64