To solve the problem of finding the value of \( x \) in each quadrilateral, we need to use the property that the sum of the interior angles of a quadrilateral is always
360 degrees. This property holds true for all types of quadrilaterals (e.g., squares, rectangles, parallelograms, trapezoids, etc.).
The general formula for the sum of the interior angles of a quadrilateral is:
\[
\text{Sum of interior angles} = 360^\circ
\]
We will apply this formula to each quadrilateral in the image and solve for \( x \).
---
Step-by-Step Solutions:
####
Quadrilateral 1:
The given angles are:
- \( 90^\circ \)
- \( 120^\circ \)
- \( 70^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
90^\circ + 120^\circ + 70^\circ + x = 360^\circ
\]
Simplify:
\[
280^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 280^\circ = 80^\circ
\]
Answer for Quadrilateral 1:
\[
\boxed{80}
\]
---
####
Quadrilateral 2:
The given angles are:
- \( 110^\circ \)
- \( 80^\circ \)
- \( 90^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
110^\circ + 80^\circ + 90^\circ + x = 360^\circ
\]
Simplify:
\[
280^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 280^\circ = 80^\circ
\]
Answer for Quadrilateral 2:
\[
\boxed{80}
\]
---
####
Quadrilateral 3:
The given angles are:
- \( 100^\circ \)
- \( 120^\circ \)
- \( 60^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
100^\circ + 120^\circ + 60^\circ + x = 360^\circ
\]
Simplify:
\[
280^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 280^\circ = 80^\circ
\]
Answer for Quadrilateral 3:
\[
\boxed{80}
\]
---
####
Quadrilateral 4:
The given angles are:
- \( 130^\circ \)
- \( 90^\circ \)
- \( 70^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
130^\circ + 90^\circ + 70^\circ + x = 360^\circ
\]
Simplify:
\[
290^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 290^\circ = 70^\circ
\]
Answer for Quadrilateral 4:
\[
\boxed{70}
\]
---
####
Quadrilateral 5:
The given angles are:
- \( 140^\circ \)
- \( 100^\circ \)
- \( 60^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
140^\circ + 100^\circ + 60^\circ + x = 360^\circ
\]
Simplify:
\[
300^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 300^\circ = 60^\circ
\]
Answer for Quadrilateral 5:
\[
\boxed{60}
\]
---
####
Quadrilateral 6:
The given angles are:
- \( 150^\circ \)
- \( 90^\circ \)
- \( 70^\circ \)
- \( x \)
Using the sum of the interior angles:
\[
150^\circ + 90^\circ + 70^\circ + x = 360^\circ
\]
Simplify:
\[
310^\circ + x = 360^\circ
\]
Solve for \( x \):
\[
x = 360^\circ - 310^\circ = 50^\circ
\]
Answer for Quadrilateral 6:
\[
\boxed{50}
\]
---
Final Answers:
\[
\boxed{80, 80, 80, 70, 60, 50}
\]
Parent Tip: Review the logic above to help your child master the concept of angles in a quadrilateral worksheet.
