Questions: the measure of the missing angle.

Transcript text: the measure of the missing angle.

Solution

Solution Steps

Step 1: Identify the type of angle

The given problem involves finding the measure of the missing angle \( a \). The diagram shows two lines intersecting, forming an angle of 42° and another angle \( a \).

Step 2: Recognize the relationship between the angles

The two angles form a linear pair, meaning they are adjacent and their non-common sides form a straight line. The sum of angles in a linear pair is always 180°.

Step 3: Set up the equation

Since the sum of the angles in a linear pair is 180°, we can write the equation: \[ a + 42° = 180° \]

Step 4: Solve for the missing angle \( a \)

Subtract 42° from both sides of the equation to find \( a \): \[ a = 180° - 42° \] \[ a = 138° \]