Angle Rules and Proofs
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Angle Rules and Proofs — Free MYP3 Mathematics Practice Questions

1QuestionSolving Problems with Justification and ProofConcept Practice
2 marks~3 minCriterion A
The diagram shows two parallel lines cut by a transversal. Angle a=65°a = 65° is formed at the first parallel line. Angle bb is formed at the second parallel line, in the same position relative to the transversal.
a
Identify the relationship between ∠a\angle a and ∠b\angle b. [1]
b
Explain why ∠b=65°\angle b = 65°, using the relationship named in part (a). [1]

Solutions

2QuestionAlternate Interior and Exterior AnglesAssessment Practice
3 marks~5 minCriterion A
Two parallel lines are cut by a transversal. One alternate interior angle measures 65∘65^\circ and the other is labelled xx.
a
Calculate the value of xx. [1]
b
Explain why alternate interior angles are equal when two parallel lines are cut by a transversal. [1]
c
A student claims that if x=90∘x = 90^\circ, both parallel lines would be perpendicular to the transversal. Do you agree? Justify your answer. [1]
Question diagram

Solutions

3QuestionAlternate Interior and Exterior AnglesConcept Practice
2 marks~3 minCriterion B
The diagram shows two parallel lines cut by a transversal. Three pairs of alternate interior angles are formed:

- First pair: 30°30° and 30°30°
- Second pair: 50°50° and 50°50°
- Third pair: 70°70° and 70°70°
a
Describe the pattern shown by the three pairs of angle measurements. [1]
b
Explain the general relationship between alternate interior angles when two parallel lines are cut by a transversal. [1]
Question diagram

Solutions

4QuestionAlternate Interior and Exterior AnglesAssessment Practice
4 marks~6 minCriterion D
A city planner is checking whether Main Street and Oak Avenue are parallel. Elm Street crosses both roads. A surveyor measures the alternate interior angle at Main Street as 118°118° and the alternate interior angle at Oak Avenue as 116°116°.
a
State the relationship between alternate interior angles when two lines are parallel. Are the two streets parallel? Justify your answer. [2]
b
Explain two real-world factors that could cause the 2°2° difference in the measured angles, even if the streets were designed to be parallel. [2]

Solutions

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