Question

4.7 assignment
find the values of x and y.

x=

y=

Explanation:

Step1: Use the property of isosceles triangle

Since the triangle is isosceles (two sides are equal), the base - angle theorem states that the base angles are equal. Also, the exterior angle property: the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
We know that \(3y=(x - 2)+(4x + 10)\) (exterior angle property). And from the base - angle theorem (the two non - exterior interior angles of the isosceles triangle), we first solve for \(x\) using the angle - sum property of a linear pair. The sum of an interior angle \((4x + 10)\) and its adjacent exterior angle \((3y)\) and the other non - adjacent interior angle \((x - 2)\) can also be related. But a more straightforward way is:
The sum of the interior angles of a triangle: \((x - 2)+(x - 2)+(4x + 10)=180\) (angle - sum property of a triangle, \(180^{\circ}\) for the sum of interior angles).
Simplify the left - hand side:

$$
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$$

Step2: Substitute \(x = 29\) into the exterior - angle formula

Substitute \(x = 29\) into \(3y=(x - 2)+(4x + 10)\)

$$
LATEXBLOCK1
$$

Answer:

\(x = 29\), \(y = 51\)