Question

1. find the value of x and y

Explanation:

Step1: Use the property of isosceles triangle

Since the two sides of the triangle are equal, the base - angles are equal. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Also, for the isosceles triangle, the angle adjacent to \((x - 2)^{\circ}\) (let's call it \(A\)) and the other non - adjacent interior angle are equal.
We know that \(4x+10=(x - 2)+(x - 2)\) (by the exterior angle property of a triangle).

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This is wrong. Let's use another property. The sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). Also, in an isosceles triangle, the two base - angles are equal.
The adjacent interior angle to \((4x + 10)^{\circ}\) is \(180-(4x + 10)=170-4x\).
Since the triangle is isosceles, \(x-2 = 170-4x\)

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Another approach:
Since the triangle is isosceles, the two base - angles are equal.
We know that \(3y=(x - 2)+(x - 2)\) (exterior angle property) and also, using the angle - sum property of a linear pair for the angle \((4x + 10)^{\circ}\) and its adjacent interior angle.
The adjacent interior angle to \((4x+10)\) is \(180-(4x + 10)=170-4x\).
Since the triangle is isosceles \(170-4x=x - 2\)

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Now, substitute \(x = 34.4\) into \(3y = 2(x - 2)\)

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Answer:

\(x = 34.4,y = 21.6\)