All the angles required to complete each sentence are:
- m ∠ 4 = 60, m ∠ 2 = 120
- m ∠ 3 = 110, m ∠ 4 = 70
- m ∠ 2 = x, m ∠ 1 = 180 - x
How to find measures of missing angles by Euclidean geometry
In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:
- If m ∠ 5 = 60, then m ∠ 4 = 60 by alternal internal angles between parallel lines and m ∠ 2 = 120 by supplementary angles.
- If m ∠ 7 = 110, then m ∠ 3 = 110 by corresponding angles between parallel lines and m ∠ 4 = 70 by supplementary angles.
- If m ∠ 6 = x, then m ∠ 2 = x by corresponding angles and m ∠ 1 = 180 - x by supplementary angles.
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