Math Problem Statement
Solution
To solve for and in this figure, we will use the properties of vertically opposite angles.
-
The expressions and represent two vertically opposite angles, which are equal. Thus, we set up the equation:
-
Rearrange to solve for :
-
Now, substitute back into one of the angle expressions (for example, ) to find the angle value:
-
Since vertically opposite angles are equal, both and equal .
-
For the value of , observe that is the supplementary angle to (since they form a straight line), so:
Final answers:
Would you like further details or have any questions?
Here are some related questions for additional practice:
- What is the sum of angles around a point?
- How do you identify vertically opposite angles?
- How can you solve for unknowns in equations involving angles?
- What are supplementary angles, and how are they related?
- How does rearranging equations help in solving for unknowns?
Tip: Always remember that vertically opposite angles are equal. This property is particularly useful when working with intersecting lines.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Vertically Opposite Angles
Supplementary Angles
Formulas
Vertically opposite angles are equal: (10x + 68)° = (13x + 53)°
Supplementary angles: z = 180° - 118°
Theorems
Vertically Opposite Angles Theorem
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10