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Circle theorems, tangent angles and regular polygon exterior angles
Free examples and worked answers. No account needed.
Practise the method.
Circle theorems, tangent angles and regular polygon exterior angles
Optional extension: Circle theorems, tangent angles and regular polygon exterior angles
Example 1
ABCD is a cyclic quadrilateral. Opposite angles A and C are (2x+31)∘ and (3x+59)∘. Find angle C.
Cyclic quadrilateralDiagram not to scaleShow worked answer
Answer: 113
- Opposite angles sum to 180∘.
- Thus (2x+31)+(3x+59)=180, or 5x+90=180.
- This gives x=18.
- Substituting into angle C gives 113∘.
Example 2
A regular polygon has 8 sides. The marked exterior angle is (x+40)∘. Find x.
Regular polygonDiagram not to scaleShow worked answer
Answer: 5
- Each exterior angle is 8360=45∘.
- Hence x+40=45, giving x=5.
Example 3
ABCD is a cyclic quadrilateral. Opposite angles A and C are (x+34)∘ and (2x+71)∘. Find angle A.
Cyclic quadrilateralDiagram not to scaleShow worked answer
Answer: 59
- Opposite angles sum to 180∘.
- Thus (x+34)+(2x+71)=180, or 3x+105=180.
- This gives x=25.
- Substituting into angle A gives 59∘.
Put it into practice.
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