0580

Angles in Polygons and Parallel Lines

Geometry

Using the shape's own properties

  • Any triangle's three angles total 180°, and knowing two gives the third by subtraction
  • An isosceles triangle has two equal angles, and they are the ones opposite the two equal sides
    • With an apex angle of 34°, the two base angles are (180 − 34) ÷ 2 = 73° each
  • An equilateral triangle has three angles of 60°
  • Any quadrilateral's four angles total 360°
A quadrilateral with interior angles of 115, 85 and 97 degrees and one side extended, so the fourth interior angle works out at 63 degrees and the exterior angle y beside it is what the question wants
Source: Basic angle properties by Save My Exams
  • Symmetry supplies extra equal angles: a parallelogram and a rhombus have equal opposite angles, and a kite has one pair of equal opposite angles
  • A square or rectangle has four right angles
Which angles a quadrilateral's own shape makes equal: a square and a rectangle have four right angles, a parallelogram and a rhombus have equal opposite angles marked in pairs, and a kite has one pair of equal opposite angles
Source: Basic angle properties by Save My Exams
Worked example

The fourth angle of a quadrilateral

Three angles of a quadrilateral are 88°, 124° and 97°. Find the fourth angle.

Solution:

  • The four angles of any quadrilateral add to 360°
  • Add the three given: 88 + 124 + 97 = 309
  • Subtract from 360: 360 − 309 = 51
  • The fourth angle is 51°