16.1 Angle facts at a point and on a line — Practise

1. Work out $x$: $x+124=180$.

Answer: $56^\circ$

2. Angles around a point are $85^\circ$, $140^\circ$ and $y^\circ$. Find $y$.

Answer: $135^\circ$

3. Two lines cross. One angle is $47^\circ$. Find the other three angles.

Answer: $47^\circ$, $133^\circ$, $133^\circ$

4. Angles on a line are $(3x+10)^\circ$ and $(2x+20)^\circ$. Find $x$ and both angl

Answer: $x=30$; the angles are $100^\circ$ and $80^\circ$.

5. Four angles around a point are $x^\circ$, $2x^\circ$, $90^\circ$ and $30^\circ$.

Answer: $x=80^\circ$

6. Explain why the angle next to $136^\circ$ on a straight line is $44^\circ$.

Answer: $44^\circ$; angles on a straight line sum to $180^\circ$.

7. A rectangle has a perimeter of $30$ cm and length $9$ cm. Find its width.

Answer: $6$ cm. Use perimeter facts from earlier geometry.

8. Two vertically opposite angles are $(4x+5)^\circ$ and $(6x-25)^\circ$. Find $x$.

Answer: $x=15$