Math Problem Statement
Solution
Let's go through the problem step by step.
Given Information:
- The quadrilateral has a straight line .
- .
- Angle .
- Angle .
- Angle .
- We need to find angles and .
Solution:
Part (a): Find the size of angle
Since , we can use the concept of corresponding angles. In this configuration, angles and are corresponding angles. Hence,
So, .
Part (b)(i): Find the size of angle
To find angle , we use the fact that the angles around point (angles , , and ) should add up to because they form a straight line.
Substitute the known values:
So, .
Part (b)(ii): Give a reason for your answer
The reason for angle being is that the angles around a straight line sum up to . Therefore, we used this property to calculate based on the given angles and .
Would you like further clarification on any part of the solution?
Related Questions:
- What is the significance of parallel lines in angle calculations?
- How do corresponding angles help in determining unknown angles in parallel line setups?
- Can you explain how angles around a straight line sum up to ?
- How would the solution change if and were not parallel?
- What other properties of quadrilaterals can help in solving angle-related problems?
Tip:
Always look for parallel lines and corresponding angles in geometry problems involving quadrilaterals and transversals; they often simplify the solution process significantly.
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Math Problem Analysis
Mathematical Concepts
Plane Geometry
Angles
Parallel Lines
Quadrilaterals
Formulas
Sum of angles around a point = 180 degrees
Properties of corresponding angles in parallel lines
Theorems
Corresponding Angles Theorem
Angles around a straight line sum to 180 degrees
Suitable Grade Level
Grades 8-10
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