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This quiz introduces a number of advanced shortcuts for solving angle chasing challenges like a pro.

*Three Key Strategies:*

1) **Start at the target angle and work out the fastest approach.**
Don't just use the angles you’re given, to find practically every angle in the picture until the target angle happens to be one of them.

2) **Draw in more lines if they're useful.**
If the given angles are far away (across the picture) from the goal, frequently, drawing one or more strategic lines will allow you to solve the puzzle very quickly.

3) **Don’t evaluate the arithmetic until you need to. (Use variables.)**
Don’t solve for the exact value of each angle in the middle unless you need to; frequently you’ll wind up adding 180 or 90 only to subtract it later. Just leave the algebra unevaluated until you’re actually forced to solve for numbers.

Find the measure of \(\angle Z.\)

**Shortcut strategy hint:** You don’t have to find the measure of the yellow angles in this picture in order to find the measure of \(\angle Z.\)

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How can we express the measure of angle \(x?\)

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Find the measure of \(\angle X.\)

**Shortcut strategy hint:** This problem can be solved in moments if you draw in just the right line!

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What is the measure of \(\angle A\)?

**Shortcut strategy hint:** Again, there is a very fast way to solve for angle \(A\) by drawing one extra line into this picture.

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Let's redo the previous problem using variables. How can we express \(\angle w?\)

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How can we express the measure of \(\angle A?\)

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