Question

in the diagram below, lines b and c are parallel. what is the measure of angle a? type the number in the box.

Explanation:

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

The sum of angles on a straight - line is 180°. Consider the straight - line where the 45° and 65° angles and angle a are located.
Let's find the sum of the known angles: \(45^{\circ}+65^{\circ}=110^{\circ}\)

Step2: Calculate angle a

Since the sum of angles on a straight - line is 180°, we can find angle a by subtracting the sum of the known angles from 180°.
\(a = 180^{\circ}-(45^{\circ}+65^{\circ})\)
\(a=180^{\circ}-110^{\circ}\)
\(a = 70^{\circ}\)

Answer:

\(70^{\circ}\)