The Angle Sum & Exterior Angle Properties Visual
Requires the visual proof using the parallel line across the top vertex.
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Drawing a parallel line through the top vertex reveals why the three angles add up to a straight line (180°).
Prove and apply the rule that triangle interior angles sum to 180°, and related exterior angle relations.
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Introduce the concept of finding a third angle without construction.
If we know two angles of a triangle are and , can we find the third angle without drawing the triangle and measuring it?
Let's look at a clever geometric trick to figure this out.
Requires the visual proof using the parallel line across the top vertex.
Drawing a parallel line through the top vertex reveals why the three angles add up to a straight line (180°).
Formal statement of the 180-degree rule.
Worked example calculating the third angle.
Consider a triangle where two of the angles are known: and . Find the measure of the third missing angle, let's call it .
MCQ to calculate a missing third angle.
A triangular piece of stained glass has two known base angles of and . What is the measure of the third angle at the top vertex?
Define the exterior angle and relate it to interior angles.
If you take any side of a triangle and extend it outward past the vertex, you create a new angle outside the triangle.
The angle formed between the extension of a side and the adjacent side is called an exterior angle.
Calculate an exterior angle given two remote interior angles.
An exterior angle of a triangle is always equal to the sum of its two interior opposite angles. If a triangle has two opposite interior angles measuring and , we can find the exterior angle without finding the third interior angle first. We simply write the equation: Exterior Angle = + 65. Solving this equation, the exterior angle is ^\circ.