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- Exterior and Interior Opposite Angles
In triangle XYZ below on the left (Fig. 9.2.1), the exterior angle is “a” and the two opposite interior angles are x and y.
To prove that a = x + y:
Draw a line at Z (i.e. line ZW) to divide the exterior angle “a” into angles p and q and let this line be parallel to line XY (see Fig. 9.2.2).
∴ a = p + q ……….(1)
From the diagram on the right (Fig. 9.2.2),
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