PSHS NCE Angles and Basic Geometry Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Angles and Basic Geometry

See the shapes, not just the words. This reviewer uses simple diagrams to teach angle relationships and basic plane-geometry ideas in a Grade 6–7 friendly way.

Diagrams included Grade 6–7 friendly Regular practice Quick Fire + Mastery

Learn Visual Guide Examples Try With Me Practice Quick Fire Mastery

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Angles and Basic Geometry

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Basic ideas to keep in mind

Point = exact location
Line segment = has two endpoints
Ray = starts at one point and goes on in one direction
Angle = formed by two rays with the same endpoint

Quick facts:
Right angle = 90°
Straight angle = 180°
Full turn = 360°
Angles in a triangle = 180°

VISUAL GUIDE

See the relationships

COMPLEMENTARY ANGLES

Complementary angles add up to 90°.

SUPPLEMENTARY ANGLES

Supplementary angles add up to 180°.

VERTICAL ANGLES

Vertical angles are equal.

TRIANGLE ANGLE SUM

The interior angles of a triangle total 180°.

WORKED EXAMPLES

Six patterns you should recognize

1. Identify angle types

An angle measuring 35° is acute. An angle measuring 90° is a right angle. An angle measuring 135° is obtuse.

2. Complementary angles

x + 37 = 90

Subtract 37 from 90.

x = 53°

3. Supplementary angles

x + 125 = 180

Subtract 125 from 180.

x = 55°

4. Vertical angles

If one angle in an X-shaped intersection is 72°, the vertical angle across from it is also 72°.

Vertical angles are equal.

5. Angles in a triangle

48 + 67 + x = 180

Add 48 and 67 to get 115. Then 180 − 115 = 65.

x = 65°

6. Parallel and perpendicular lines

Parallel lines never meet. Perpendicular lines meet to form a right angle.

Shortcut: If the corner is 90°, the lines are perpendicular.

TRY WITH ME

Which relationship is it?

Two angles form a straight line. One angle is 146°. What is the other angle?

1. A straight line means the two angles are supplementary.
2. Supplementary angles add to 180°.
3. 180 − 146 = 34.

34°

COMMON TRAPS

Watch out for these

Mixing up complementary and supplementary.
Complementary = 90°. Supplementary = 180°.

Forgetting triangle angle sum.
Angles inside a triangle always total 180°.

Not recognizing vertical angles.
Opposite angles in an X-shape are equal.

Using a picture only by appearance.
Use the given measurements and facts, not just how “big” the drawing looks.

REGULAR PRACTICE

Build the skill

These mix angle types, complementary, supplementary, vertical angles, triangle angles, and line relationships.

QUICK FIRE

Can you spot the angle fact fast?

Five quick questions. Use the shortest valid idea.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Still mixing up angle relationships?

Send Teacher Abi your result or the exact item that confused you. I can help you see which geometry fact to use first.

Message Teacher Abi

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