Math Problem Statement
Solution
The image shows a pair of scissors, where angles are marked. Angle is given, and we need to find the other three angles (, , and ).
Solution:
-
Angles and appear to be vertical angles, which means they are congruent (equal in measure). Therefore:
-
Angles and are also vertical angles, meaning:
-
The sum of the angles on a straight line is . Since and are adjacent on the straight line formed by the scissors, we have: Substituting : Thus: And since , we also have:
Final answers:
Would you like more details or have any questions?
Here are 5 related questions:
- What are vertical angles and why are they always congruent?
- Can angles in any other type of figure be considered vertical angles?
- How do we calculate unknown angles on a straight line?
- What is the sum of angles around a point?
- How do adjacent angles relate to complementary and supplementary angles?
Tip: Remember that vertical angles are always equal, and angles on a straight line sum to 180°, which is useful in many geometry problems.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Angles
Vertical Angles
Supplementary Angles
Formulas
m∠1 + m∠2 = 180° (adjacent angles on a straight line)
Vertical angles are congruent (m∠1 = m∠3, m∠2 = m∠4)
Theorems
Vertical Angles Theorem
Linear Pair Postulate
Suitable Grade Level
Grades 6-8