19. Angle Types and Special Sums

Angle vocabulary makes problems faster.

Useful sums:

• Right angle: \(90^\circ\)
• Straight line: \(180^\circ\)
• Full turn around a point: \(360^\circ\)
• Complementary angles add to \(90^\circ\)
• Supplementary angles add to \(180^\circ\)

Common mistake: using \(180^\circ\) for angles around a point. A full point is \(360^\circ\).

Deepen your understanding
Use this focused guide to turn Angle Types and Special Sums into a dependable GED® problem-solving skill.

Learning targets

• Classify acute, right, obtuse, straight, reflex, and full-turn angles.
• Use complementary, supplementary, and around-a-point sums.
• Estimate angle size before solving an equation.

Step-by-step solving routine

1. Identify the vertex and the two rays that form the angle.
2. Choose the correct benchmark sum: (90^°), (180^°), or (360^°).
3. Write an equation that includes every part of the benchmark angle.
4. Solve and compare the answer with the sketch's acute or obtuse appearance.

GED® application
If two angles form a straight line and one is (128^°), the other is (180^°-128^°=52^°). The drawing should show one obtuse and one acute angle, confirming the result.

Coach check
Never trust a diagram to be perfectly to scale, but do use its broad angle type as a reasonableness check.

Visual study gallery
Study each diagram before the worked examples. Name what is measured, identify the needed dimensions or relationships, and explain which formula or rule the picture supports.

10 worked examples and problem solving
Use these examples as guided practice before attempting the session MCQs. Each problem is self-contained, including any needed table or context.

Example 1
Problem: What is the complement of a \(25\)-degree angle?
Answer: \(65^\circ\)
Solution: Complementary angles add to \(90^\circ\): \(90 - 25 = 65\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 2
Problem: What is the supplement of a \(70\)-degree angle?
Answer: \(110^\circ\)
Solution: Supplementary angles add to \(180^\circ\): \(180 - 70 = 110\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 3
Problem: What is the complement of a \(42\)-degree angle?
Answer: \(48^\circ\)
Solution: Complementary angles add to \(90^\circ\): \(90 - 42 = 48\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 4
Problem: What is the supplement of a \(135\)-degree angle?
Answer: \(45^\circ\)
Solution: Supplementary angles add to \(180^\circ\): \(180 - 135 = 45\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 5
Problem: How many degrees are in a straight?
Answer: \(180^\circ\)
Solution: A straight measures \(180^\circ\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 6
Problem: How many degrees are in a full point?
Answer: \(360^\circ\)
Solution: A full point measures \(360^\circ\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 7
Problem: How many degrees are in a right angle?
Answer: \(90^\circ\)
Solution: A right angle measures \(90^\circ\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 8
Problem: What is the complement of a \(18\)-degree angle?
Answer: \(72^\circ\)
Solution: Complementary angles add to \(90^\circ\): \(90 - 18 = 72\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 9
Problem: What is the supplement of a \(88\)-degree angle?
Answer: \(92^\circ\)
Solution: Supplementary angles add to \(180^\circ\): \(180 - 88 = 92\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Example 10
Problem: Angles around a point include \(110^\circ\), \(95^\circ\), and x degrees. What is x?
Answer: \(155^\circ\)
Solution: Angles around a point add to \(360^\circ\): \(360 - 110 - 95 = 155\). Pro tip: memorize \(90\), \(180\), and \(360\) as anchor angles.

Additional resources

• Angle anchors: right angle \(90^\circ\), straight line \(180^\circ\), full turn \(360^\circ\).
• Complement/supplement drill: complementary adds to 90; supplementary adds to 180.