Question 8 of 12intermediate🔧 ApplyDiagram4 marks

Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.

Correct Answer

To construct a rectangle where a diagonal divides opposite angles into 50° and 40°: Step 1: Draw a line segment AB of arbitrary length. Step 2: At point A, construct a line making 50° (or 40°) with AB. Step 3: At point B, construct a perpendicular to AB. Step 4: The intersection gives point C. Step 5: Complete the rectangle by constructing perpendiculars at A and C. Step 6: The diagonal from A to C will divide angle A into 50° and 40°, and similarly divide angle C. Verify by measuring the angles.

Exercise: Construct | Q: 1 | (Page Page 25)
For More Understanding

Explanation

This follows the same method as the 60°-30° construction. The diagonal divides the 90° angle into two parts summing to 90°. For 50° and 40°, construct the appropriate angle at one corner and complete the rectangle.

Solution Steps

  1. Step 1: Draw AB of chosen length.

  2. Step 2: At A, construct 50° angle with AB.

  3. Step 3: At B, construct perpendicular.

  4. Step 4: Mark intersection as C.

  5. Step 5: Complete rectangle.

  6. Step 6: Verify angle divisions by diagonal.

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