Parallel lines, triangle angles and the triangle inequality
Answers are for parents and teachers.
1
The lines are parallel and one angle is 60°, as shown. Find all the other angles and say which kinds of pair they make.
Every angle is 60° or 120°. At each crossing the top right and bottom left angles are 60° (vertically opposite); the top left and bottom right angles are 120° (on a straight line with 60°). The two top right angles are corresponding, and so are all matching pairs at the two crossings.
2
The lines are parallel and two corresponding angles are (3x − 20)° and (x + 40)°. Find x and the angles.
3x − 20 = x + 40, 2x = 60, x = 30. Each angle is 70°.
3
The angles of a triangle are x, (x + 20)° and (x + 40)°. Find x and the three angles.
3x + 60 = 180, so x = 40. The angles are 40°, 60° and 80°.
4
In triangle ABC the exterior angle at C is 130° and the interior angle at A is 50°. Find the interior angle at B and the interior angle at C.
B = 130° − 50° = 80°. The interior angle at C = 180° − 130° = 50°. Check: 50 + 80 + 50 = 180.
5
Can (7, 9, 15) be the sides of a triangle? Can (7, 8, 15)? Give the reason.
(7, 9, 15): 7 + 9 = 16 > 15, yes. (7, 8, 15): 7 + 8 = 15, not greater, so no.