Chapter 16 Review

Resolve the chapter problem

The pattern can be solved by applying each angle fact in turn. At the straight path, adjacent angles total $180^\circ$. At a crossing, vertically opposite angles match. Parallel borders let you transfer corresponding or alternate angles, while co-interior angles total $180^\circ$. The triangular tile has interior sum $180^\circ$. State the fact beside every calculation, then check the total fits the shape.

Mixed practice

For each question, choose the method and give a reason.

1. Two lines cross. One angle is $62^\circ$. Find the other three.
2. A transversal crosses parallel lines. One angle is $73^\circ$. Find its alternate angle and co-interior angle.
3. A triangle has angles $41^\circ$, $x^\circ$ and $(x+19)^\circ$. Find $x$.
4. A quadrilateral has angles $85^\circ$, $95^\circ$, $110^\circ$ and $x^\circ$. Find $x$.
5. Find each interior angle of a regular octagon.
6. An exterior angle of a regular polygon is $40^\circ$. Find the number of sides.
7. Earlier learning: solve $4x+7=31$.
8. Higher only: prove that the exterior angle of a triangle equals the sum of its two opposite interior angles.

Reflect

Write one angle fact you can now explain with a reason. Which question made you choose between two possible methods? Note what helped you decide.