Before you read

Answer first — see what you already know.

A triangular road sign has two angles measuring $45°$ and $75°$ . What is the third angle?

A
$50°$
B
$60°$
C
$70°$
D
$80°$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

In a structural truss, an exterior angle of a triangle is $130°$ . The two remote interior angles are $x °$ and $(x + 30) °$ . Find $x$ .

A
40
B
50
C
60
D
65

Check your answer

Answer:

Theory

Key Triangle Theorems

Triangle Angle Sum: The three interior angles of ANY triangle sum to $180°$ .
$a + b + c = 180°$

Triangle angle sum = 180°

Exterior Angle Theorem: An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
$\text{Exterior angle} = \text{sum of remote interior angles}$

Triangle Inequality: The sum of any two sides must be greater than the third side.
$a + b > c, \quad a + c > b, \quad b + c > a$

Example 1

A triangle has angles $50°$ , $65°$ , and $x°$ . Find $x$ .

$50 + 65 + x = 180$

$x = 65°$

x = 65°

Common Mistakes

Common Mistakes to Avoid

Forgetting that the angles of a triangle sum to 180

^{\circ}

, not 360

^{\circ}

360 $^{\circ}$ is the sum of angles around a point.

Remember: avoid this error.

Triangle inequality

Don't forget to check ALL three combinations.

Remember: avoid this error.

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