Lynn Byrd, Greg Byrd and, Chris Pearce Solutions for Chapter: Angles and Constructions, Exercise 3: Exercise 5.2

Look at the diagram. Explain why these two lines cannot be parallel.

This shape is made from eight identical triangles. Sketch the diagram and label the other angles equal to $a, b$ or $c$.

This shape is made from eight identical triangles. Use this fact to calculate the missing angles.

The diagram shows angle $X$ is $45°$. Calculate $a$.

The diagram shows angle $X$ is $45°$. Angle $X$ is increased to $90°$. Find the new value of $a$.

The diagram shows angle $X$ is $45°$. Angle $X$ is increased to $119°$. Find the new value of $a$.

The diagram shows angle $X$ is $45°$. Can angle $X$ be more than $119°$? Give a reason for your answer.

This trapezium has a pair of parallel sides. Use this fact to calculate the missing angles.