To find the missing angles, we use the formula for the sum of interior angles of a polygon:
Sum = (n - 2) × 180°, where *n* is the number of sides.
Problem 1:
This is a quadrilateral (4 sides). Sum = (4-2) × 180° = 360°.
Given angles: 135°, 60°, 50°.
x = 360° - (135° + 60° + 50°) = 360° - 245° = 115°.
Problem 2:
This is a quadrilateral (4 sides). Sum = 360°.
There are two right angles (90° each), one 50° angle, and x°.
x = 360° - (90° + 90° + 50°) = 360° - 230° = 130°.
Problem 3:
This is a triangle (3 sides). Sum = 180°.
The tick marks on the sides indicate it is an isosceles triangle. The angles opposite the equal sides are equal. The base angle given is 60°. Therefore, the other base angle is also 60°.
x = 180° - (60° + 60°) = 180° - 120° = 60°.
(Note: This is actually an equilateral triangle).
Problem 4:
This is a heptagon (7 sides). Sum = (7-2) × 180° = 5 × 180° = 900°.
Given angles: 130°, 122°, 130°, 130°, 128°, 138°.
Sum of known angles = 130+122+130+130+128+138 = 778°.
x = 900° - 778° = 122°.
Problem 5:
This is a pentagon (5 sides). Sum = (5-2) × 180° = 3 × 180° = 540°.
There are two right angles (90° each), one 120° angle, one 107° angle, and x°.
Sum of known angles = 90 + 90 + 120 + 107 = 407°.
x = 540° - 407° = 133°.
Problem 6:
This is a quadrilateral (4 sides). Sum = 360°.
Given angles: 50°, 140°, 70°.
x = 360° - (50° + 140° + 70°) = 360° - 260° = 100°.
Problem 7:
This is a parallelogram (quadrilateral). Sum = 360°.
In a parallelogram, opposite angles are equal and consecutive angles add to 180°.
We see angles 60°, 60°, 120°, and x°. Wait, looking closely at the image for #7.
Top-left is x°. Top-right is 60°. Bottom-left is 60°. Bottom-right is 120°.
Actually, let's re-examine #7. It looks like a parallelogram.
Bottom-left = 60°. Top-right = 60°. These are opposite angles, so they match.
Bottom-right = 120°. Top-left = x°. These are opposite angles.
So x must be 120°.
Let's check the sum: 60 + 60 + 120 + 120 = 360°. Correct.
Alternatively, consecutive angles sum to 180°. x + 60 = 180 -> x = 120. Or x + 120? No, x is top left, 60 is top right. They are consecutive. So x + 60 = 180 => x = 120.
Wait, let me look at the image again carefully.
#7: Top-left is x°. Top-right is 60°. Bottom-left is 60°. Bottom-right is 120°.
If it's a parallelogram, opposite angles are equal.
Top-left (x) should equal Bottom-right (120). So x = 120.
Top-right (60) should equal Bottom-left (60). This matches.
Consecutive angles: Top-left (x) + Top-right (60) = 180? 120+60=180. Yes.
So x = 120°.
Problem 8:
This is a rhombus/kite shape (quadrilateral). Sum = 360°.
Given angles: 140° (top), 40° (left), 140° (bottom), x° (right).
Sum of known angles = 140 + 40 + 140 = 320°.
x = 360° - 320° = 40°.
(Check: In a kite/rhombus, opposite angles might be equal or adjacent. Here top/bottom are 140, left is 40, so right must be 40 to make sum 360).
Final Answer:
1. x° = 115°
2. x° = 130°
3. x° = 60°
4. x° = 122°
5. x° = 133°
6. x° = 100°
7. x° = 120°
8. x° = 40°
Parent Tip: Review the logic above to help your child master the concept of exterior angles of a polygon worksheet.
