Question

draw a hexagon that has two right angles. draw a hexagon that has two acute angles.

Explanation:

for Drawing a Hexagon with Two Right Angles:

Step1: Recall Hexagon Properties

A hexagon has 6 sides and the sum of interior angles is \((6 - 2)\times180^{\circ}=720^{\circ}\). We need to create 6 - sided figure with 2 right angles (\(90^{\circ}\) each).

Step2: Sketch the Base

Draw a horizontal line segment (let's say length \(a\)) as the first side.

Step3: Add First Right Angle

At the right - end of the first segment, draw a vertical line segment (length \(b\)) upwards, forming a right angle (\(90^{\circ}\)) with the first segment.

Step4: Add Second Right Angle

From the top - end of the vertical segment, draw a horizontal line segment (length \(c\)) to the right, forming a right angle with the vertical segment (this is the second right angle).

Step5: Connect the Remaining Sides

Now, we need to draw 3 more sides to close the hexagon. Let's draw a line segment downwards at an angle from the end of the third segment, then a line segment to the left at an angle, and finally a line segment downwards (or at an appropriate angle) to connect back to the start of the first segment. The non - right angles can be adjusted so that the sum of all interior angles is \(720^{\circ}\). For example, if the two right angles are \(90^{\circ}\) each, the remaining 4 angles should sum to \(720 - 2\times90=540^{\circ}\), so each of the remaining angles (on average) would be \(135^{\circ}\), but they can be adjusted as long as the total is correct and the figure is a closed 6 - sided polygon.

for Drawing a Hexagon with Two Acute Angles:

Step1: Recall Angle Definitions

An acute angle is less than \(90^{\circ}\). The sum of interior angles of a hexagon is \(720^{\circ}\).

Step2: Start Sketching

Draw a line segment. At one end, draw a segment that forms an acute angle (say \(60^{\circ}\)) with the first segment.

Step3: Add the Second Acute Angle

A few sides later (e.g., after 2 more sides), draw a segment that forms another acute angle (say \(70^{\circ}\)) with the previous segment.

Step4: Close the Hexagon

Draw the remaining sides, ensuring that the sum of all interior angles is \(720^{\circ}\). So if the two acute angles are \(60^{\circ}\) and \(70^{\circ}\), the remaining 4 angles should sum to \(720-(60 + 70)=590^{\circ}\), and each of these angles can be obtuse (greater than \(90^{\circ}\)) or right, as long as the total sum is maintained and the figure is a closed 6 - sided polygon.

(Note: Since drawing is a visual task, the above steps provide a guide for constructing the hexagons. The actual drawing can be done on paper or using a drawing tool by following the angle and side - length guidelines to form a closed 6 - sided figure with the specified number of right or acute angles.)

For the answer, since it's a drawing task, the key is to follow the steps above to create the respective hexagons. The final answer in terms of the drawing is the two hexagons constructed as per the step - by - step guides (one with two right angles and one with two acute angles).

Answer:

for Drawing a Hexagon with Two Acute Angles:

Step1: Recall Angle Definitions

An acute angle is less than \(90^{\circ}\). The sum of interior angles of a hexagon is \(720^{\circ}\).

Step2: Start Sketching

Draw a line segment. At one end, draw a segment that forms an acute angle (say \(60^{\circ}\)) with the first segment.

Step3: Add the Second Acute Angle

A few sides later (e.g., after 2 more sides), draw a segment that forms another acute angle (say \(70^{\circ}\)) with the previous segment.

Step4: Close the Hexagon

Draw the remaining sides, ensuring that the sum of all interior angles is \(720^{\circ}\). So if the two acute angles are \(60^{\circ}\) and \(70^{\circ}\), the remaining 4 angles should sum to \(720-(60 + 70)=590^{\circ}\), and each of these angles can be obtuse (greater than \(90^{\circ}\)) or right, as long as the total sum is maintained and the figure is a closed 6 - sided polygon.

(Note: Since drawing is a visual task, the above steps provide a guide for constructing the hexagons. The actual drawing can be done on paper or using a drawing tool by following the angle and side - length guidelines to form a closed 6 - sided figure with the specified number of right or acute angles.)

For the answer, since it's a drawing task, the key is to follow the steps above to create the respective hexagons. The final answer in terms of the drawing is the two hexagons constructed as per the step - by - step guides (one with two right angles and one with two acute angles).