16.3 Angles in triangles and quadrilaterals — Practise

1. A triangle has angles $48^\circ$, $73^\circ$ and $x^\circ$. Find $x$.

Answer: $59^\circ$

2. The opposite interior angles of a triangle are $42^\circ$ and $69^\circ$. Find t

Answer: $111^\circ$

3. A quadrilateral has three angles $90^\circ$, $105^\circ$, $83^\circ$. Find the f

Answer: $82^\circ$

4. Triangle angles are $x^\circ$, $(x+20)^\circ$ and $60^\circ$. Find $x$.

Answer: $x=50$; the angles are $50^\circ$, $70^\circ$, $60^\circ$.

5. A quadrilateral has angles $x^\circ$, $2x^\circ$, $100^\circ$ and $80^\circ$. Fi

Answer: $x=60^\circ$

6. A triangle has opposite interior angles $35^\circ$ and $78^\circ$. Find the exte

Answer: $113^\circ$; an exterior angle equals the sum of the two opposite interior angles.

7. Two parallel lines give co-interior angles $x^\circ$ and $4x^\circ$. Find both a

Answer: $x=36$; the angles are $36^\circ$ and $144^\circ$.

8. A quadrilateral has angles $90^\circ$, $90^\circ$, $90^\circ$ and $x^\circ$. Fin

Answer: $90^\circ$; splitting the quadrilateral into two triangles gives $360^\circ$.