Question

"Find the measure of angle x in Rectangle JKLM.

a) 115°
b) 65°
c) 90°
d) 180°"

Answer 1

The measure of angle J (and angle L) is 90°, making the correct answer for angle x in Rectangle JKLM (c) 90°.

The correct answer is (c) 90°.

Step-by-step explanation:

In a rectangle, opposite angles are equal, and the sum of all interior angles is 360°. Since JKLM is a rectangle, angles J and L are opposite angles, and angles K and M are opposite angles. Therefore, angles J and L have the same measure, as do angles K and M.

Let's denote the measure of angle J
`(or angle L) as \(\angle J\).`Similarly, let's denote the measure of angle K (or angle M) as
`\(\angle K\)`. Since opposite angles are equal,
`\(\angle J = \angle L\) and \(\angle K = \angle M\).`

The sum of all interior angles in a rectangle is 360°. Therefore, we can write the equation:

`\[ \angle J + \angle K + \angle L + \angle M = 360° \]`

Substitute in the fact that
`\(\angle J = \angle L\) and \(\angle K = \angle M\):`

`\[ \angle J + \angle K + \angle J + \angle K = 360° \]`

Combine like terms:

`\[ 2\angle J + 2\angle K = 360° \]`

Divide both sides by 2:

`\[ \angle J + \angle K = 180° \]`

Since
`\(\angle J = \angle L\) and \(\angle K = \angle M\),` we can rewrite this as:

`\[ \angle J + \angle L = 180° \]`

Now, since
`\(\angle J = \angle L\),` we can substitute:

`\[ 2\angle J = 180° \]`

Divide both sides by 2:

`\[ \angle J = 90° \]`

Therefore, the measure of angle J (and angle L) is 90°, making the correct answer for angle x in Rectangle JKLM (c) 90°.