KA-0088Angles on lines, in triangles, in polygons
3 points, difficulty 1 of 3Level 5–6about 45sThree angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
A quadrilateral's angles add to 360.
2The strategy
Add the three angles you are given, then take the total from 360. Nothing about the shape of the quadrilateral matters — the sum is the same for every one.
3The full solution
80 + 95 + 110 = 285, and 360 - 285 = 75.
Solution— no shortcut on this one
The four angles of any quadrilateral add to 360 degrees. The three given add to 80 + 95 + 110 = 285, so the fourth is 360 - 285 = 75 degrees. The transferable idea: the angle sum of an n-sided polygon is (n - 2) times 180, which gives 180 for a triangle and 360 for a quadrilateral.
Why this is on the test: Using 180 instead of 360 is the single most common angle-sum error once shapes get more than three sides.