Part of a proof that co-interior angles on parallel lines add up to 180° is shown below.
Fill in the gaps by choosing from the options provided in the boxes. You may use each option more than once.
[tex]x + y = 180[/tex] because 1 2.
[tex]y = z[/tex] because 1 2.
Therefore [tex]x + z = 180[/tex] so co-interior angles add up to 180°.
Options for 1:
- angles on a straight line
- angles around a point
- angles in a triangle
- vertically opposite angles
- corresponding angles
- alternate angles
Options for 2:
- are equal
- add up to 180°
- add up to 360°
Answer (2)
In the problem, we are looking to fill in the gaps in the proof that shows co-interior angles on parallel lines add up to 18 0 ∘ . Let's fill in each gap step-by-step.
The first statement is x + y = 180 because angles on a straight line add up to 180° . When two angles are formed on a straight line, their sum is always 18 0 ∘ .
The second statement is y = z because alternate angles are equal . When two parallel lines are cut by a transversal, the alternate angles are equal.
Finally, from these two statements, we can conclude x + z = 180 , showing that the co-interior angles add up to 18 0 ∘ .
Therefore, using the properties of angles on a straight line and the equality of alternate angles, we can prove that co-interior angles on parallel lines sum to 18 0 ∘ . This is a fundamental property in geometry used to understand the behavior of parallel lines when intersected by a transversal.
The proof that co-interior angles on parallel lines add up to 18 0 ∘ involves showing that the angles formed on a straight line equal 18 0 ∘ and that alternate angles are equal. Thus, combining these properties leads to the conclusion that co-interior angles also sum to 18 0 ∘ . This is fundamental for understanding geometric relationships with parallel lines.
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