16.5 Geometrical reasoning and proof — Practise

1. Parallel lines give one angle of $64^\circ$. Find and justify the co-interior an

Answer: $116^\circ$; co-interior angles sum to $180^\circ$.

2. A triangle has angles $52^\circ$, $x^\circ$ and $(x+20)^\circ$. Find $x$, showin

Answer: $x=54^\circ$; triangle angles sum to $180^\circ$.

3. Three quadrilateral angles are $88^\circ$, $94^\circ$ and $101^\circ$. Find the

Answer: $77^\circ$; quadrilateral angles sum to $360^\circ$.

4. Two lines cross. One angle is $x+18$ degrees and its opposite is $3x-22$ degrees

Answer: $x=20$; vertically opposite angles are equal.

5. A triangle has opposite interior angles $x^\circ$ and $(x+30)^\circ$. Its exteri

Answer: $x=50$; the exterior angle equals the sum of the opposite interior angles.

6. A regular polygon has exterior angle $24^\circ$. Find its number of sides and ex

Answer: 15 sides; exterior angles total $360^\circ$.

7. Find each interior angle of a regular decagon.

Answer: $144^\circ$; use $(n-2)180^\circ$ then divide by $n$.

8. A triangle sits on a straight line. Its base angles are $x^\circ$ and $(x+20)^\c

Answer: $x=55$; base angles are $55^\circ$ and $75^\circ$, and the third is $50^\circ$.