if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles, and angle 1 = 71 degrees, find angle 3

Answer 1

Vertical angles are the opposite angles formed by two intersecting lines,

and they are always equal in measurement.

Thus, the vertical angles, <1 and <2, are congruent. (<1 ≅ <2)

Complementary angles are angles that add up to 90º.

Thus, <2 + <3 = 90º.

Since <1 = 71° and <1 = <2, <2 is also 71°.

Substitute <2 with 71° in the equation <2 + <3 = 90º:

71° + <3 = 90°

Subtract 71° from both sides of the above equation:

<3 = 90° - 71° = 19°

Therefore, the measurement of <3 is 19°.

Answer 2

Hello,

Since angle 1 and angle 2 are vertical, they have the same measure. So angle 2 = angle 1 = 71 degrees.

Also, since angle 2 and angle 3 are complementary, they add up to 90 degrees: angle 2 + angle 3 = 90 degrees. So 71 + angle 3 = 90 degrees. That means angle 3 = 19 degrees.

Recap: angle 2 = 71 degrees; angle 3 = 19 degrees.