Geometry Worksheets | Polygons Worksheets - Free Printable

To find the missing angle in each quadrilateral, we use a simple rule: The sum of all interior angles in any four-sided shape (quadrilateral) is always $360^\circ$.

So, for every problem, we add up the three angles we know and subtract that total from $360$ to find the missing one.

Here are the step-by-step calculations for each number:

1)
* Known angles: $71.4^\circ + 59.1^\circ + 96.2^\circ = 226.7^\circ$
* Missing angle ($\angle BAD$): $360^\circ - 226.7^\circ = \mathbf{133.3^\circ}$

2)
* Known angles: $92.8^\circ + 82.0^\circ + 90.4^\circ = 265.2^\circ$
* Missing angle ($\angle CDA$): $360^\circ - 265.2^\circ = \mathbf{94.8^\circ}$

3)
* Known angles: $90.4^\circ + 100.5^\circ + 95.1^\circ = 286.0^\circ$
* Missing angle ($\angle BCD$): $360^\circ - 286.0^\circ = \mathbf{74.0^\circ}$

4)
* Known angles: $68.6^\circ + 114.5^\circ + 81.2^\circ = 264.3^\circ$
* Missing angle ($\angle BCD$): $360^\circ - 264.3^\circ = \mathbf{95.7^\circ}$

5)
* Known angles: $75.8^\circ + 102.7^\circ + 86.7^\circ = 265.2^\circ$
* Missing angle ($\angle BAD$): $360^\circ - 265.2^\circ = \mathbf{94.8^\circ}$

6)
* Known angles: $125.5^\circ + 99.2^\circ + 66.7^\circ = 291.4^\circ$
* Missing angle ($\angle ABC$): $360^\circ - 291.4^\circ = \mathbf{68.6^\circ}$

7)
* Known angles: $84.6^\circ + 110.4^\circ + 72.6^\circ = 267.6^\circ$
* Missing angle ($\angle ABC$): $360^\circ - 267.6^\circ = \mathbf{92.4^\circ}$

8)
* Known angles: $94.9^\circ + 72.3^\circ + 97.2^\circ = 264.4^\circ$
* Missing angle ($\angle CDA$): $360^\circ - 264.4^\circ = \mathbf{95.6^\circ}$

9)
* Known angles: $89.3^\circ + 76.0^\circ + 102.8^\circ = 268.1^\circ$
* Missing angle ($\angle CDA$): $360^\circ - 268.1^\circ = \mathbf{91.9^\circ}$

10)
* Known angles: $99.3^\circ + 73.7^\circ + 97.7^\circ = 270.7^\circ$
* Missing angle ($\angle ABC$): $360^\circ - 270.7^\circ = \mathbf{89.3^\circ}$

11)
* Known angles: $58.3^\circ + 103.2^\circ + 109.3^\circ = 270.8^\circ$
* Missing angle ($\angle BAD$): $360^\circ - 270.8^\circ = \mathbf{89.2^\circ}$

12)
* Known angles: $99.1^\circ + 88.8^\circ + 74.7^\circ = 262.6^\circ$
* Missing angle ($\angle BCD$): $360^\circ - 262.6^\circ = \mathbf{97.4^\circ}$

Final Answer:
1) $\angle BAD = 133.3^\circ$
2) $\angle CDA = 94.8^\circ$
3) $\angle BCD = 74.0^\circ$
4) $\angle BCD = 95.7^\circ$
5) $\angle BAD = 94.8^\circ$
6) $\angle ABC = 68.6^\circ$
7) $\angle ABC = 92.4^\circ$
8) $\angle CDA = 95.6^\circ$
9) $\angle CDA = 91.9^\circ$
10) $\angle ABC = 89.3^\circ$
11) $\angle BAD = 89.2^\circ$
12) $\angle BCD = 97.4^\circ$