Question

find the values of the missing angles in the diagram below.
show your work here
w =
x =
y =
z =

Explanation:

Step1: Find the value of \(x\)

Since the two - arrowed lines are parallel, and the angle of \(82^{\circ}\) and \(x\) are corresponding angles. Corresponding angles formed by parallel lines are equal. So \(x = 82^{\circ}\).

Step2: Find the value of \(y\)

The angle of \(33^{\circ}\) and \(y\) are vertical angles. Vertical angles are equal. So \(y=33^{\circ}\).

Step3: Find the value of \(z\)

We know that the sum of angles in a triangle is \(180^{\circ}\). In the triangle with angles \(z\), \(68^{\circ}\) and the angle adjacent to \(y\) (which is also \(33^{\circ}\) because vertical angles are equal). So \(z=180-(68 + 33)=79^{\circ}\).

Step4: Find the value of \(w\)

The angle of \(82^{\circ}\) and the angle adjacent to \(w\) are supplementary (linear - pair, sum to \(180^{\circ}\)). Let the adjacent angle to \(w\) be \(a\), so \(a = 180 - 82=98^{\circ}\). Then, using the angle - sum property of a triangle with angles \(a\), \(33^{\circ}\) and \(w\), we have \(w=180-(98 + 33)=49^{\circ}\).

Answer:

\(w = 49^{\circ}\), \(x = 82^{\circ}\), \(y = 33^{\circ}\), \(z = 79^{\circ}\)