Which of the following can be four interior angles of a quadrilateral?

Options

A. `140°, 40°, 20°, 160°`
B. `270°, 150°, 30°, 20°`
C. `40°, 70°, 90°, 60°`
D. `110°, 40°, 30°, 180°`

Answer

To determine which of the given options can be the four interior angles of a quadrilateral, we need to remember two important properties of quadrilaterals:

1. The sum of the interior angles of a quadrilateral is always 360 degrees.
2. No angle in a quadrilateral can be equal to or greater than 180 degrees.

Now, let's analyze each option step by step.

### Step 1: Analyze the Options

**Option 1:** 140°, 40°, 20°, 160°

- Calculate the sum:
\[ 140 + 40 + 20 + 160 = 360 \text{ degrees} \]
- Check if any angle is 180° or more:
- All angles are less than 180°.

**Conclusion:** This option is valid.

---

**Option 2:** 270°, 150°, 30°, 20°

- Calculate the sum:
\[ 270 + 150 + 30 + 20 = 470 \text{ degrees} \]
- Since 470° is greater than 360°, this option is invalid.

---

**Option 3:** 40°, 70°, 90°, 60°

- Calculate the sum:
\[ 40 + 70 + 90 + 60 = 260 \text{ degrees} \]
- Since 260° is less than 360°, this option is invalid.

---

**Option 4:** 110°, 40°, 30°, 180°

- Calculate the sum:
\[ 110 + 40 + 30 + 180 = 360 \text{ degrees} \]
- Check if any angle is 180° or more:
- The angle 180° is present, which means it cannot form a quadrilateral.

**Conclusion:** This option is invalid.

### Final Answer

After analyzing all options, the only valid set of angles that can form a quadrilateral is from **Option 1: 140°, 40°, 20°, 160°**.

---