Grade 8 Mathematics

Triangle Geometry & Pythagoras — Quiz 1

Exam-style questions covering angles of triangles, exterior angles, and the Theorem of Pythagoras. Based on Question 4 of the standard Grade 8 paper. Enter your name to begin.

Please enter your name to start.

What this quiz covers

Grade 8 — Triangle Geometry & Pythagoras Quiz 1 draws its questions at random from a bank of 7 questions. A full worked solution is shown after you answer each one.

Example questions

A sample of the questions you will practise in this quiz. Work them out yourself - the full solution appears after you answer each one.

  1. In the diagram, \(CA\) is produced (extended) beyond \(A\). The angle of \(130^\circ\) and angle \(x\) lie on this straight line at \(A\). Calculate the value of \(x\).
  2. Which reason correctly justifies the size of \(x\) in the diagram?
  3. In \(\triangle ABC\): the angle at \(A\) is \(x = 50°\), the angle at \(C\) is \(y°\), and the angle at \(B\) is \((y - 20)°\). Calculate the value of \(y\).
  4. In \(\triangle ABC\), \(y = 75°\) and the angle at \(B\) is \((y - 20)°\). Calculate the size of \(\hat{B}\).
  5. In the diagram, \(PQ = QR\) and \(PS \perp QR\) (so \(\hat{S} = 90°\)). \(PQ = 15\) and \(PS = 9\). Calculate the length of \(QS\).