Two angles decide the third
A triangular island is where three roads meet. A faded board gives two of its corners: 40° and 75°. You can find the third without a protractor.
Step 1 of 3
- A triangle, three corners.
- Two corners are known: 40° and 75°. The third is a question mark.
- 180° − 40° − 75° = 65°. The question mark is gone.
Subtract the two you know from 180
The three corners add to 180°. So the third corner is 180 minus the other two.
Take two corners, 90° and 35°. First, 180 − 90 = 90. Then 90 − 35 = 55. The third corner is 55°.
Two corners must add to less than 180°. If they add to 180° or more, no triangle exists. 130° and 60° add to 190°. So they cannot be two corners of one triangle.
Pick the third corner. Then see it measured.
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