13.4 sum of angles _1allr

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Sum of the angles

The sum of the three angles in a triangle is 180°
The sum of the four angles in a quadrilateral is 360°

∠A+∠B+∠C=180°

∠D+∠E+∠F+∠G=360°

Calculating angles

You can use the sum of the angles and your knowledge of special triangles and quadrilaterals to calculate unknown angles.

Calculating angles

Calculate the size of angle C.

What size is angle C?

1. ∠C=360−82−60=218°
2. ∠C=82+60=142°
3. ∠C=180−82−60=38°
4. ∠C=​3​​(82+60)​​=37°

Calculating angles

The angle sum of a triangle is 180°

∠C=180−82−60=38°

Calculating angles

Quadrilateral DEFG is a rhombus.
Calculate the size of angle G.

What size is angle G?

1. ∠G=245°
2. ∠G=115°
3. ∠G=65°
4. ∠G=57.5°

Calculating angles

Quadrilateral DEFG is a rhombus
The angle sum of a quadrilateral is 360°
A rhombus has rotation and reflection symmetry, therefore the opposite angles are equal.

∠D=∠F=115°

∠G=∠E=​2​​(360−115−115)​​=​2​​130​​=65°

Equal angles in triangle and quadrilaterals

Isosceles triangle: 2 angles (base angles) are the same size
Equilateral triangle: all 3 angles are the same size (60°)
Rhombus/Parallelogram: opposite angles are equal
Kite: 2 angles are the same size (on either side of the axis of symmetry)
Square/Rectangle: all 4 angles are the same size (90°)

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