Question

find the values of x, y, and z.
answer attempt 1 out of 2
x =
y =
z =

Explanation:

Step1: Use triangle - angle - sum property

The sum of interior angles of a triangle is 180°. For the large triangle, \(x + 40+80 + 30=180\).

Step2: Solve for x

Simplify the left - hand side of the equation: \(x+(40 + 80+30)=x + 150\). Then \(x+150 = 180\), so \(x=180 - 150=30\).

Step3: For the small triangle with angles 80, y, and the angle adjacent to 40

The angle adjacent to 40 is \(180 - 40=140\). Using the angle - sum property for this small triangle: \(80 + y+140=180\). But this is wrong. Let's use another approach. For the non - overlapping part of the large triangle with angles \(x\), \(y\), and 30, since \(x = 30\), then \(30+y + 30=180\), so \(y=180-(30 + 30)=120\).

Step4: For angle z

For the triangle with angles 40, z, and the angle adjacent to y. The angle adjacent to y is \(180 - 120 = 60\). Using the angle - sum property: \(40+z + 60=180\), so \(z=180-(40 + 60)=80\).

Answer:

\(x = 30\)
\(y = 120\)
\(z = 80\)