Answer :
Certainly! To draw a quadrilateral with three angles of the same size and each angle less than 180°, follow these steps:
1. Choose the size for the three equal angles:
Let's choose an angle measure that is convenient and ensures all angles are less than 180°. For example, we can choose 80° for each of the three equal angles.
2. Calculate the fourth angle:
The sum of the interior angles in any quadrilateral is always 360°. Therefore, we can find the fourth angle by subtracting the sum of the three equal angles from 360°.
\( 3 \times 80° = 240° \)
\( 360° - 240° = 120° \)
3. Draw the quadrilateral:
- Start by drawing one angle of 80° at a point.
- Then draw two connected lines from the ends of this angle to form another 80° angle at each end. This will form two adjacent angles of 80° each.
- Now, from one of these lines, draw another 80° angle such that you have three angles of 80° drawn consecutively.
- Finally, join the ends of these lines with a line segment to complete the quadrilateral, ensuring the last angle is 120°.
The resulting quadrilateral will have three angles each measuring 80° and the fourth angle measuring 120°, all of which satisfy the given conditions:
```
D
/ \
80° / \ 80°
/ \
C-------A
120° B
```
1. Choose the size for the three equal angles:
Let's choose an angle measure that is convenient and ensures all angles are less than 180°. For example, we can choose 80° for each of the three equal angles.
2. Calculate the fourth angle:
The sum of the interior angles in any quadrilateral is always 360°. Therefore, we can find the fourth angle by subtracting the sum of the three equal angles from 360°.
\( 3 \times 80° = 240° \)
\( 360° - 240° = 120° \)
3. Draw the quadrilateral:
- Start by drawing one angle of 80° at a point.
- Then draw two connected lines from the ends of this angle to form another 80° angle at each end. This will form two adjacent angles of 80° each.
- Now, from one of these lines, draw another 80° angle such that you have three angles of 80° drawn consecutively.
- Finally, join the ends of these lines with a line segment to complete the quadrilateral, ensuring the last angle is 120°.
The resulting quadrilateral will have three angles each measuring 80° and the fourth angle measuring 120°, all of which satisfy the given conditions:
```
D
/ \
80° / \ 80°
/ \
C-------A
120° B
```
