Question

find the values of angles a - c in the diagram to the right
a. m∠a =
b. m∠b =
c. m∠c =

Explanation:

Step1: Use alternate - interior angles

The angle of \(72^{\circ}\) and \(\angle c\) are alternate - interior angles. So \(m\angle c = 72^{\circ}\).

Step2: Use the property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In the triangle with angles \(a\), \(b\), and \(39^{\circ}\), and we know that the exterior - angle property can also be used. The angle adjacent to \(72^{\circ}\) in the triangle is \(180 - 72=108^{\circ}\).
We know that \(m\angle a + 39^{\circ}=72^{\circ}\) (exterior - angle property of a triangle: an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles). So \(m\angle a=72^{\circ}-39^{\circ}=33^{\circ}\).

Step3: Calculate angle \(b\)

Using the fact that the sum of angles in a triangle is \(180^{\circ}\). In the triangle with angles \(a = 33^{\circ}\), \(b\), and \(39^{\circ}\), we have \(m\angle b=180^{\circ}-33^{\circ}-39^{\circ}=108^{\circ}\).

Answer:

a. \(m\angle a = 33^{\circ}\)
b. \(m\angle b = 108^{\circ}\)
c. \(m\angle c = 72^{\circ}\)