Question

9. In the given figure, AC = BC and <ACY = 150° Find x and y.​

Answer 1

Answer:

x = y = 105°

Step-by-step explanation:

Because AC = BC, Triangle ABC is isosceles.

So, angleBAC = angleABC

angleACY = 150°

So, angleBAC + angleABC = 150° (Exterior Angle Property)

angleBAC = angleABC = 75°

So, x = 180° - 75° = 105°

And, y = 180° - 75° = 105°

Answer 2

Answer:

x = y =105°

Step-by-step explanation:

Given: ∠ACY = 150°, AC = BC

∠ACY + ∠ACB = 180 ( linear pair )

150 + ∠ACB = 180

∠ACB = 180 - 150

∴ ∠ACB = 30°

As AC = BC, ∠CAB = ∠ABC ( isosceles triangle property )

Let ∠CAB = ∠ABC = z

∠ACB + ∠CAB + ∠ABC = 180 ( Angle sum property of triangles )

30 + z + z = 180

2z + 30 = 180

2z = 180 - 30

2z = 150

z = 150 / 2

z = 75

z = ∠CAB = ∠ABC = 75°

As ∠CAB = ∠ABC, ∠x = ∠y

x + ∠ABC = 180 ( linear pair )

x + 75 = 180

x = 180 - 75

x = 105°

∴ x = y = 105°

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