Question

a right angle intersects a line at point m.
which statement is true about angles 1 and 2?

they are congruent.
they are right angles.
they are complementary.
they are supplementary.

Explanation:

Identify the geometric components

The image shows a straight line passing vertically through point \(M\). A right angle is positioned with its vertex at point \(M\). This right angle is situated between two rays that form angles with the vertical line: angle 1 at the top and angle 2 at the bottom.

Set up the angle relationship

A straight line forms a straight angle, which measures exactly \(180^\circ\). The straight angle along the vertical line is composed of three adjacent angles: angle 1, the right angle, and angle 2.

Formulate the equation

Using the Angle Addition Postulate, we can write the sum of these three adjacent angles along the straight line:

$$ m\angle 1 + 90^\circ + m\angle 2 = 180^\circ $$

Solve for the sum of angles 1 and 2

Subtract \(90^\circ\) from both sides of the equation to find the relationship between angle 1 and angle 2:

$$ m\angle 1 + m\angle 2 = 90^\circ $$

Determine the correct terminology

By definition, two angles whose measures add up to \(90^\circ\) are called complementary angles. Therefore, angles 1 and 2 are complementary.

Answer:

• They are congruent.
• They are right angles.
• They are complementary. (Correct answer)
• They are supplementary.