Question

14. Find the measures of all the angles in the rectangle. 1 2 3 5 32 4

Answer 1

`90^(0) - 32^(0) = 58^(0)`

1 = 4 = 90°

2 = 32°

3 = 5 = 58°

Answer 2

• ∠1 = ∠4 = 90°
• ∠2 = 32°
• ∠3 = ∠5 = 58°

Explanation:

You want the measures of the marked angles in the rectangle, given one of the acute angles is 32°.

Complementary angles

The corner angles of a rectangle are all 90°. That's part of the definition of a rectangle:

∠1 = ∠4 = 90°

That make angles 5 and 32° be complementary angles:

∠5 = 90° -32° = 58°

The angles at the opposite end of the diagonal are complementary to these, as the sum of angles in a triangle is 180°.

∠2 = 90° -58° = 32°

∠3 = 90° -32° = 58°

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Additional comment

You may have noticed that angles on opposite sides and opposite ends of the diagonal have the same measure. This is no coincidence. These are called "alternate interior angles". As such, they are always congruent where a diagonal meets parallel lines. (The sides of a rectangle are parallel.)