Grade 8 Angles of Triangles Quiz 1 draws its questions at random from 8 questions across these topics:
A few of the question types, with full solutions, so you know what to expect.
Angle Sum of a Triangle. In triangle ABC, the interior angles are \((4x + 10)°\), \((5x + 5)°\) and \(2x°\). What is the value of \(x\)?
Answer: \(x = 15°\)
The angles of a triangle sum to 180°.
\((4x+10) + (5x+5) + 2x = 180\)
\(11x + 15 = 180\)
\(11x = 165\)
\(x = 15°\)
The angles are: \(4(15)+10 = 70°\), \(5(15)+5 = 80°\), \(2(15) = 30°\).
Classifying Triangles — Isosceles. Triangle DEF has DE = DF (indicated by tick marks) and EF = 10 cm. What type of triangle is DEF?
Answer: Isosceles triangle
The tick marks show DE = DF — two sides of the triangle are equal in length.
A triangle with exactly two equal sides is called an isosceles triangle.
Property: the base angles of an isosceles triangle are equal, so ∠DEF = ∠DFE.
Angle Sum — Isosceles Triangle. In triangle GHJ, ∠G = 22° and ∠J = 22°. What is the size of angle H?
Answer: 136°
Since ∠G = ∠J = 22°, the sides opposite these angles are equal (HJ = GH = 7 cm).
This means triangle GHJ is isosceles.
Using the angle sum of a triangle:
\(\angle H = 180° - \angle G - \angle J = 180° - 22° - 22°\)
\(\angle H = 136°\)
Exterior Angle Theorem. Points J, K, L, M lie on a straight line. Using the exterior angle theorem, what is the value of \(x\)?
Answer: 70°
The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
∠NLM is an exterior angle of triangle KLN:
\((2x - 30) = (2x - 80) + (x - 20)\)
\(2x - 30 = 3x - 100\)
\(70 = x\)
Check at K (angles on a straight line): \((2y-10)+(2x-80)=180°\) → \(y = 65°\).
Angles in a Right Triangle. AD ⊥ BC so ∠ADB = 90°. Given ∠B = 41°, what is the value of angle \(y\) (i.e. ∠BAD)?
Answer: 49°
In triangle ABD: ∠B + ∠ADB + ∠BAD = 180°
\(41° + 90° + y = 180°\)
\(131° + y = 180°\)
\(y = 49°\)