Find the value of x in each polygon by calculating the missing interior angle.

To solve these problems, we need to find the value of $x$ in each polygon. The key idea is that the sum of all interior angles in a polygon depends on how many sides it has.

The formula for the sum of interior angles of a polygon with $n$ sides is:

> Sum = (n - 2) × 180°

Once we know the total sum, we can subtract the known angles and solve for $x$.

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Problem 1: Quadrilateral (4 sides)

Angles given: 104°, 130°, 76°, and $x$

Step 1: Find total sum of interior angles for a quadrilateral.

Sum = (4 - 2) × 180° = 2 × 180° = 360°

Step 2: Add up the known angles.

104 + 130 + 76 = 310°

Step 3: Subtract from total to find $x$.

$x = 360 - 310 = 50°$

✔ Check: 104 + 130 + 76 + 50 = 360 → Correct.

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Problem 2: Pentagon (5 sides)

Angles given: 120°, 131°, 100°, 70°, and $x$

Step 1: Total sum for pentagon.

Sum = (5 - 2) × 180° = 3 × 180° = 540°

Step 2: Add known angles.

120 + 131 + 100 + 70 = 421°

Step 3: Solve for $x$

$x = 540 - 421 = 119°$

✔ Check: 120 + 131 + 100 + 70 + 119 = 540 → Correct.

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Problem 3: Pentagon (5 sides)

Angles given: 121°, 113°, and three angles labeled $x$ (so three angles are equal)

Step 1: Total sum = 540° (same as above)

Step 2: Let’s write the equation.

121 + 113 + x + x + x = 540
→ 234 + 3x = 540

Step 3: Solve for $x$

3x = 540 - 234 = 306
x = 306 ÷ 3 = 102°

✔ Check: 121 + 113 + 102 + 102 + 102 = 540 → Correct.

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Problem 4: Quadrilateral (4 sides)

Angles given: 94°, 104°, and two angles labeled $x$, plus one right angle (90° — marked with square)

Wait — let’s look again.

Actually, looking at the shape: it’s a quadrilateral with angles: 94°, 104°, 90°, and $x$

Step 1: Total sum = 360°

Step 2: Add known angles.

94 + 104 + 90 = 288°

Step 3: Solve for $x$

$x = 360 - 288 = 72°$

✔ Check: 94 + 104 + 90 + 72 = 360 → Correct.

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Final Answers:

1. $x = 50$
2. $x = 119$
3. $x = 102$
4. $x = 72$

Final Answer:
1. 50
2. 119
3. 102
4. 72