Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Simplex wikipedia , lookup

Rotation formalisms in three dimensions wikipedia , lookup

Pythagorean theorem wikipedia , lookup

History of trigonometry wikipedia , lookup

Multilateration wikipedia , lookup

Rational trigonometry wikipedia , lookup

Trigonometric functions wikipedia , lookup

Integer triangle wikipedia , lookup

Euclidean geometry wikipedia , lookup

Euler angles wikipedia , lookup

Transcript
```Angles of Triangles
The angles inside a polygon are called interior angles.
When the sides of a polygon are extended, other angles are formed. The angles
outside the polygon that are adjacent to the interior angles are called exterior
angles.
The sum of the interior angle measures of a triangle is 180°.
∠𝐴 + ∠𝐵 + ∠𝐶 = 180°
To find the measure of an interior angle of a triangle:
𝑥 + 29°
90°
𝑥°
Step 1 – Copy the formula
∠𝐴 + ∠𝐵 + ∠𝐶 = 180°
Step 2 – Fill in the values known
90° + (𝑥 + 29)° + 𝑥° = 180°
Step 3 - Solve
119 + 2𝑥 = 180
−119
− 119
2𝑥 = 61
2𝑥
2
61
= 2
𝑥 = 30.5
The measures of the 3 angles are:
90°
30.5°
30.5 − 29 = 59.5°
This answer can be checked by adding all 3 angles: 90 + 30.5 + 59.5 = 180
MA08
3-2
To find the measure of an exterior angle of a triangle:
The measure of an exterior angle of a triangle is equal to the sum of the measures of
𝑥°
∠𝑧 = ∠𝑥 + ∠𝑦
𝑦°
𝑧°
Example:
Find the measure of ∠𝑧
87°
51.8°
𝑧°
Step 1 – Copy the formula
∠𝑧 = ∠𝑥 + ∠𝑦
Step 2 – Fill in the values known
𝑧 = 87 + 51.8
Step 3 - Solve
𝑧 = 138.8
The measure of ∠𝑧 𝑖𝑠 138.8°
MA08
3-2
```