Question

find the value of X and Y in figure​

Answer 1

Answer:

x=57°

Step-by-step explanation:

=>114°+y=180° (linear pair axiom)

=>y=180°-114

=>y=66°

=>x+x+66°=180° (angle sum property of the triangle)

=>2x+66°=180°

=>x=114°/2

=>x=57°

HERE IS YOUR ANSWER IS X=57°

Answer 2

Explanation:

In the solution, we shall be mainly using two properties:

1. The property of a Linear Pair, that is, if any two angles form a straight line or a straight angle, their sum is equal to 180°.
2. The Exterior Angle Property, which states that when an exterior angle is drawn from one of the angles, the measure of the exterior angle is equal to the sum of the other two angles.

Now let's have a look at the figure. We can see that ∠ACD is the exterior angle formed by extending BC, meaning

∠ACD = ∠CAB + ∠ABC

==> x + x = 114°

==> 2x = 114°

==> x = 114/2

∴ x = 57°

Now, ∠ACD and ∠ACB form a linear pair, meaning

∠ACD +  ∠ACB = 180°

==> 114° + y = 180°

==> y = 180° 114°

∴ y = 66°

∴ The values of x and y are 57° and 66° respectively.

Answer: x = 57°, y = 66°

I hope this helps. :D