KA-0080Properties of triangles and quadrilaterals
4 points, difficulty 2 of 3Level 5–6about 75sAn isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Could there be two angles of 100?
2The strategy
In an isosceles triangle two angles are equal. Check first whether the 100 can be one of the equal pair — the angle sum decides that for you — and then split what is left.
3The full solution
Two angles of 100 would already be 200, more than the 180 a triangle has. So 100 is the odd one out, and the other two share 80 equally: 40 each.
Solution— no shortcut on this one
An isosceles triangle has two equal angles. If 100 were one of the pair, two of them would already total 200, which is more than the 180 a triangle has — impossible. So the 100 is the odd angle out, and the other two share 180 - 100 = 80 between them, giving 40 each. Check: 100 + 40 + 40 = 180. The transferable idea: check which angle can be the repeated one before dividing anything.
Why this is on the test: Isosceles questions turn on deciding which angle is the repeated one, and an obtuse angle settles it immediately for a student who checks.