Question

find angle measures of parallel lines and transversals
the figure above shows two horizontal lines and two intersecting transversals.
what is the value of a?
what is the value of b?
what is the value of c?

Explanation:

Step1: Use angle - sum property of a straight - line

The sum of angles on a straight - line is 180°. For the straight - line with the 45° angle and angle \(a\), we have \(a + 45^{\circ}=180^{\circ}\).

$$a=180^{\circ}- 45^{\circ}$$

Step2: Use the property of corresponding angles

The 73° angle and angle \(b\) are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So \(b = 73^{\circ}\).

Step3: Use the property of vertical angles

Angle \(c\) and the angle adjacent to the 73° angle (on the upper - parallel line) are vertical angles. First, find the adjacent angle to the 73° angle on the upper - parallel line. The sum of adjacent angles on a straight - line is 180°, so the adjacent angle to 73° is \(180^{\circ}-73^{\circ}=107^{\circ}\). Since vertical angles are equal, \(c = 107^{\circ}\).

Answer:

\(a = 135^{\circ}\)
\(b = 73^{\circ}\)
\(c = 107^{\circ}\)