Question

find the measure of the missing angle.
answer attempt 1 out of 2
a =

Explanation:

Step1: Identify angle relationship

The angles form a linear pair? No, wait, actually, the two angles (a and 140°) and the straight line? Wait, no, looking at the diagram, the angle adjacent to 140° and angle \( a \) should be supplementary? Wait, no, maybe it's a straight angle? Wait, no, the diagram shows that the angle of 140° and angle \( a \) are adjacent and form a linear pair? Wait, no, actually, if we assume that the two outer rays are forming a straight line (180°), then the sum of \( a \) and 140° should be 180°? Wait, no, maybe I misread. Wait, the diagram: there are three rays, with one angle labeled 140° and angle \( a \). Wait, actually, the straight line (180°) is formed by the two opposite rays. So the angle between the lower ray and the middle ray is 140°, and angle \( a \) is between the middle and upper ray. So \( a + 140° = 180° \)? Wait, no, that would be if they are supplementary. Wait, no, maybe the angle of 140° and angle \( a \) are adjacent and form a linear pair (sum to 180°). Wait, no, let's think again. If two angles are adjacent and form a straight line, their sum is 180°. So if one angle is 140°, the other (a) is \( 180° - 140° \).

Step2: Calculate angle \( a \)

Using the supplementary angles property (sum of angles on a straight line is 180°), we have:
\( a + 140° = 180° \)
Subtract 140° from both sides:
\( a = 180° - 140° \)
\( a = 40° \)

Answer:

\( 40^\circ \)