Geometry (higher) Flashcards
Calculate the lettered angles in this triangle
e = 55° and f = 70°
Reasoning: e is the same as the angle shown because it is an isosceles triangle.
2 x 55 = 110, 180 - 110 = 70
Find the missing angles in this quadrilateral
j = 105°, k = 75°, l = 105°
Reasoning:
j + 75° = 180° (supplementary angles)
k = 75° (opposite angles in a parallelogram)
l = 105° (opposite j)
The 3 angles of an isosceles triangle are:
2x, x - 10 and x - 10.
What is the actual size of each angle?
2x + x - 10 + x - 10 = 180 (angle sum of a triangle)
4x - 20 = 180
x = 50
So the angles are 100°, 40° and 40°
Work out the missing angle in the polygon below.
Polygon has 6 sides, so its interior angles sum to (4 x 180 =) 720°.
720 − 100 − 105 − 140 − 120 − 160 = b = 95°
You can find the sum of the interior angles of any polygon by splitting it into …
You can find the sum of the interior angles of any polygon by splitting it into …
…triangles.
You then multiply the number of triangles by 180° and you have the angle sum.
E.g. For the heptagon shown, 5 triangles means 5 x 180 = 900°.
The sum of an exterior angle and its adjacent interior angle is…
The sum of an exterior angle and its adjacent interior angle is…
…180°.
How many sides does a regular polygon have if its exterior angle is 15°?
360 ÷ 15 = 24
Exterior angles always sum to 360° so the polygon has 24 sides.
Calculate the size of the interior angle of the regular polygons with 12 sides.
Exterior angle is 360 ÷ 12 = 30°
Interior angle is 180 − 30 = 150°
How many sides does a regular polygon have if its interior angle is 162°?
Exterior angle is 180 − 162 = 18°
Number of sides is 360 ÷ 18 = 20
Calculate the values of x and y in this quadrilateral.
x + 10 + 2x - 10 = 180 (supplementary angles)
4y + 5 + 2y - 5 = 180 (also supplementary angles)
Solving both equations gives x = 60° and y = 30°
