Question

In the rectangle ABCD, ∠CAB = 28°

The measure of angle y is:

पर्याय

• 144°

• 124°

• 120°

• 130°

Answer 1

124°

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 and its angles

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

The angles opposite the equal sides are also equal, so ∠OAB = ∠OBA.

The given angle ∠CAB = 28° is the same as ∠OAB.

∠OAB = 28°

Therefore, ∠OBA = 28°

Step 3: Solve for angle AOB

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

For ΔAOB, we can find the measure of ∠AOB.

Based on the problem and the provided solution, it is assumed that ‘y’ represents the angle ∠AOB.

∠AOB + ∠OAB + ∠OBA = 180°

y + 28° + 28° = 180°

y + 56° = 180°

Subtract 56° from both sides to find the value of y.

y = 180° – 56°

y = 124°