Question

Which angle must be complementary to angle 3?

3 lines intersect to form 6 angles. Clockwise, from top left, the angles 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3.
Angle 2
Angle 4
Angle 5
Angle 6

Answer 1

Two angles are complementary if the sum of their measures is 90 degrees.

From your description, angle 2 is 90 degrees. The other angles (1, 3, 4, 5, 6) need to be evaluated to find out which one, when added to angle 3, totals 90 degrees.

To determine which angle is complementary to angle 3, let's first analyze the situation. Since angles are formed by the intersection of the lines, angles that are adjacent (next to each other) are often related.

If angle 2 is 90 degrees and located directly next to angle 3, we can conclude that angle 3 must be 0 degrees because angle 2 is already taking the full 90 degrees.

Additionally, knowing from your description, angles 5 and 2 are both 90 degrees. Therefore, if angle 3 is along with these angles, e.g., along with angle 2 and angle 5, it also implies that angle 3 should be equal to the other angles to satisfy the criteria of complementary angles.

So angle 4 is adjacent to angle 3 and likely would be measured, determining which will effectively accumulate with angle 3 to yield 90 degrees.

To summarize:
- Angle 2 is 90 degrees, thus not complementary to angle 3.
- Angle 5 is also 90 degrees, and hence cannot be complementary to angle 3.
- Angle 6 is the angle that should add alongside angle 3 to equate to 90 degrees, given angle 4 (which we know is not adjacent in measure to add) provides a different value.

The result is that angle 4 is the most likely candidate for being complementary to angle 3.

Therefore, angle **4** must be the one that is complementary to angle **3**.