Question

what are the values of x, y, and z?
x = 111, y = and z = 75 (simplify your answers. do not include the degree symbol in your answer.)

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand triangle, the sum of interior angles of a triangle is 180°. So, \(x+45 + 24=180\) (since the third angle in the left - hand triangle is \(180-(66 + 30)=84\), and the angle adjacent to \(x\) and this 84° angle form a straight line, so the angle inside the left - hand triangle related to \(x\) is \(180 - x\), and \((180 - x)+45+24 = 180\), which simplifies to \(x=111\)).

Step2: Use angle - sum property of a triangle for the right - hand triangle

In the right - hand triangle, we know one angle is 43° and the exterior angle adjacent to \(z\) is 119°. The non - adjacent interior angles of the right - hand triangle add up to the exterior angle. First, find the third angle in the right - hand triangle. Let's call it \(a\). We know that \(z + a=119\). Also, using the angle - sum property of a triangle in the right - hand triangle with the 43° angle, if the third angle is \(a\), then \(a + 43+y=180\). The angle adjacent to 119° inside the right - hand triangle is \(180 - 119 = 61\). So, \(z=119 - 43=76\).

Step3: Calculate \(y\)

In the right - hand triangle, using the angle - sum property of a triangle (\(y+43 + 61=180\)). So, \(y=180-(43 + 61)=76\).

Answer:

\(y = 76\)