Question

In the rectangle ABCD, ∠CAB = 25°, then ∠AOB is ______.

Options

• 100°

• 110°

• 120°

• 130°

Answer 1

In the rectangle ABCD, ∠CAB = 25°, then ∠AOB is 130°.

Explanation:

Step 1: Use the properties of a rectangle

In a rectangle, the diagonals are equal in length and bisect each other.

Let the diagonals AC and BD intersect at point O. 

This means that AO = BO = CO = DO.

Step 2: Identify the isosceles triangle

Since AO = BO, the triangle ΔAOB is an isosceles triangle.

In an isosceles triangle, the angles opposite the equal sides are equal.

The angles opposite sides AO and BO are ∠OBA and ∠OAB, respectively.

Therefore, ∠OAB = ∠OBA.

Step 3: Find the angles of ΔAOB

The given angle is ∠CAB = 25°.

This is the same as ∠OAB.

∠OAB = 25°

Since ∠OAB = ∠OBA, we have:

∠OBA = 25°

The sum of the interior angles of any triangle is 180°.

For ΔAOB, we can write:

∠AOB + ∠OAB + ∠OBA = 180°

∠AOB + 25° + 25° = 180°

∠AOB + 50° = 180°

Step 4: Solve for angle AOB

Subtract 50° from both sides of the equation:

∠AOB = 180° – 50°

∠AOB = 130°