Question

find the values of x, y, and z in the triangle to the right.
x = 36
y =

Explanation:

Step1: Find the value of \(x\)

Use the property that the sum of adjacent angles forming a straight line is \(180^{\circ}\).
For the angles \(x^{\circ}\) and \((3x + 2)^{\circ}\), we have \(x+(3x + 2)=180\).
Simplify the equation: \(4x+2 = 180\).
Subtract 2 from both sides: \(4x=178\).
Divide both sides by 4: \(x = 36\).

Step2: Find the value of \(y\)

Use the property that the sum of angles in a triangle is \(180^{\circ}\).
We know one angle is \(x = 36^{\circ}\), another angle \(z\) (we'll find \(z\) first).
Since \(z+(3x - 2)=180\) (adjacent angles forming a straight line), substitute \(x = 36\): \(z+(3\times36- 2)=180\), \(z+(108 - 2)=180\), \(z + 106=180\), \(z=74\).
Now, in the triangle, \(x + y+z=180\) (angle - sum property of a triangle). Substitute \(x = 36\) and \(z = 74\): \(36+y + 74=180\).
Simplify: \(y+110=180\).
Subtract 110 from both sides: \(y = 70\).

Answer:

\(y = 70\)