Quadrilaterals and polygons
Answers are for parents and teachers.
1
The angles of a quadrilateral are (x + 20)°, (2x − 10)°, 90° and (x + 40)°. Find x and the four angles.
4x + 140 = 360, so 4x = 220 and x = 55. The angles are 75°, 100°, 90° and 95°. Check: 75 + 100 + 90 + 95 = 360.
2
ABCD is an isosceles trapezium with AB parallel to DC and angle A = 115°. Find angles B, C and D.
B = 115° (equal base angles). C and D are 180° − 115° = 65° each.
3
In parallelogram ABCD angle A = (3x + 15)° and angle B = (2x + 15)°. Find x and the four angles.
A and B are next to each other: 5x + 30 = 180, so x = 30. A = C = 105° and B = D = 75°.
4
A rhombus has a perimeter of 28 cm and angle A = 50°. Find its side, and the angle that the diagonal AC makes with the side AB.
The side is 28 ÷ 4 = 7 cm. The diagonal bisects angle A, so it makes 25° with AB.
5
The angles of a polygon add up to 1620°. How many sides does it have? Is it possible to tell if it is convex?
1620 ÷ 180 = 9, so n − 2 = 9 and n = 11. We cannot tell: the angle sum is the same for convex and concave polygons; we would need the angles.