Vertically opposite angles

Task goals

• Find the size of an angle vertically opposite a given numeric angle where two straight lines cross.
• State the rule that vertically opposite angles are equal, and correct a false statement about them, such as a claim that they add to 180 degrees.
• Solve for an unknown when two vertically opposite angles are given as algebraic expressions.
• Find all four angles formed by two intersecting lines, given only one of the four angles.
• Explain why knowing one angle in an intersecting-lines diagram is enough to find all four, and what check is needed before assuming two angles are vertically opposite.
• Solve for an unknown using both the vertically-opposite-angles rule and the adjacent-angles-are-supplementary rule together, when a vertically opposite angle and an adjacent angle are both given as algebraic expressions.
• Solve a word problem where the acute and obtuse angles formed by intersecting lines are related by a ratio or a difference, and find both angle sizes.
• Explain why vertically opposite angles remain equal when the intersecting lines are tilted or rotated, identify a measurement error in a claimed pair of vertically opposite angles, and create an original vertically-opposite-angles problem.