Question

A rectangular sheet of paper is folded at the corner like the image. Find the value of x. What’s the answer and how do you solve?

Answer 1

To find the value of x in the folded rectangular sheet of paper, we can use the properties of alternate angles formed by the folding. Let's denote the angle at the corner as y. When the paper is folded, the alternate angle formed will also be y. Since the total angle at the corner is 90⁰90⁰, we can set up the equation:

y+x=90⁰

Now, solving for x, we get:

x=90⁰−y

To determine y, we observe that it is also an interior angle in a right-angled triangle formed by the folded paper. The sum of angles in a triangle is 180⁰180⁰, so:

90⁰+90⁰+y=180⁰

Solving for y:

y=180⁰−180⁰

y=0⁰

Now, substitute y=0⁰ into the equation for x:

x=90⁰−0⁰

x=90⁰

In the folded rectangular sheet of paper, the angle x is determined to be 90⁰. This result arises from recognizing the complementary relationship between x and the angle formed by the fold, denoted as y. The total angle at the corner being 90⁰90⁰ ensures that the folded angle complements x, resulting in a clear and concise solution.

Therefore, the value of x is 90⁰.

Answer 2

x = 66°

The area folded over is a right triangle, and its void is a right triangle as well. We have one angle marked 33° and a right angle in the bottom left. This leaves us 180-(33+90) = 180-123 = 57°.

The folded over triangle has the same angle measurements.

We have two angles to the left of x, which form a straight angle with x. Straight angles have a sum of 180°. The angles that form the straight angle with x both have a measure of 57°. This gives us:

180-(57+57) = 180-114 = 66°