To solve the problem of finding the missing angles in the given diagrams, we will use basic geometric principles such as:
1.
Angles on a straight line sum to 180°.
2.
Angles around a point sum to 360°.
3.
The sum of interior angles in a triangle is 180°.
Let's solve each part step by step.
---
Problem 1:
Diagram: A straight line with one angle marked as \( x \) and another angle marked as \( 42^\circ \).
Solution:
- Angles on a straight line sum to \( 180^\circ \).
- Therefore, \( x + 42^\circ = 180^\circ \).
- Solving for \( x \):
\[
x = 180^\circ - 42^\circ = 138^\circ
\]
Answer: \( x = 138^\circ \)
---
Problem 2:
Diagram: A triangle with two angles marked as \( 50^\circ \) and \( 37^\circ \), and the third angle marked as \( x \).
Solution:
- The sum of the interior angles in a triangle is \( 180^\circ \).
- Therefore, \( 50^\circ + 37^\circ + x = 180^\circ \).
- Simplifying:
\[
87^\circ + x = 180^\circ
\]
- Solving for \( x \):
\[
x = 180^\circ - 87^\circ = 93^\circ
\]
Answer: \( x = 93^\circ \)
---
Problem 3:
Diagram: A quadrilateral with three angles marked as \( 110^\circ \), \( 120^\circ \), and \( 100^\circ \), and the fourth angle marked as \( x \).
Solution:
- The sum of the interior angles in a quadrilateral is \( 360^\circ \).
- Therefore, \( 110^\circ + 120^\circ + 100^\circ + x = 360^\circ \).
- Simplifying:
\[
330^\circ + x = 360^\circ
\]
- Solving for \( x \):
\[
x = 360^\circ - 330^\circ = 30^\circ
\]
Answer: \( x = 30^\circ \)
---
Problem 4:
Diagram: A circle with a central angle marked as \( x \) and an inscribed angle subtending the same arc marked as \( 68^\circ \).
Solution:
- The measure of a central angle is twice the measure of the inscribed angle subtending the same arc.
- Therefore, \( x = 2 \times 68^\circ \).
- Simplifying:
\[
x = 136^\circ
\]
Answer: \( x = 136^\circ \)
---
Final Answers:
\[
\boxed{138^\circ, 93^\circ, 30^\circ, 136^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of finding missing angles worksheet 7th grade.
