Questions: the measure of the missing angle.

Solution Steps

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 $a$.

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°.

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

Subtract 42° from both sides of the equation to find $a$: $$a = 180° - 42°$$ $$a = 138°$$

Final Answer