The result of the Erasmus Plus Project US ICT

1. Angles
Prepared by Arminas Baronas,
Panevezys 5th gymnasium
Prepared by
Arminas Baronas and
Armandas Kripaitis, Lithuania

2. Content
• Origin
• Identifying
• Types
• Measurements
• Units
• Tricky Place
• Internal and External Angles
• Vertical and adjacent angle pairs
• Combining angle pairs

3. Origin
The word angle comes from the Latin word
angulus, meaning "corner"; In Greek language
angle is ἀγκύλος (ankylοs), meaning ‘‘curved‘‘.

4. Identifying
In mathematical expressions, it is common
to use Greek letters (α, β, γ, θ, φ, . . . ) to
serve as variables standing for the size of
some angle.
Vertex Ray 2
α
Ray - A portion of a line which
starts at a point and goes off in a
particular direction to infinity.

5. Types

6. Types

7. Measurements in radians
In order to measure an angle θ, a circular arc
centered at the vertex of the angle is drawn.
The ratio of the length s of the arc by the radius
r of the circle is the measure of the angle in
radians.

8. Measurements in degrees
In order to measure an angle θ, a protractor is
used to find angle’s value.
30⁰
θ

9. Units(Common)
Degrees Radians

10. Tricky Place
When measuring from a line:
• a positive angle goes counterclockwise.
• a negative angle goes clockwise.

11. Internal and External Angles
The sum of the internal angle
and the external angle on the
same vertex is 180°.
The sum of the external angles of any simple
convex or non-convex polygon is 360°.
Convex - having a surface
that is curved or rounded
outward

12. Vertical angle pairs
When two straight lines intersect at
a point, four angles are formed.
A pair of angles opposite each other
are called vertical angles or opposite
angles.

13. Adjacent angle pairs
Adjacent angles are
angles that share a
common vertex and edge
but do not share any
interior points.

14. Combining angle pairs
Special angle pairs which involve the summation
of angles:
• Complementary;
• Supplementary;
• Explementary angles or conjugate angles.

15. Complementary angles
Angle pairs whose measures sum to
one right angle (1/4 turn, 90°, or π/2
radians).

16. Supplementary angles
Two angles that sum to a
straight angle (1/2 turn,
180°, or π radians).

17. Explementary (conjugate) angles
A pair of angles that
sum 360 degrees.