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Question 8.1.5: Determining Supplementary Angles If ∡ABC and ∡ABD are supple......

Determining Supplementary Angles

If ∡ABC and ∡ABD are supplementary and m∡ABC is five times larger than m∡ABD, determine m∡ABC and m∡ABD (Fig. 8.12).

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Let m∡ABD = x, then m∡ABC = 5x. Since these angles are supplementary, we have

m∡ABD + m∡ABC = 180°

x + 5x = 180°

6x = 180°

x = 30°

Thus, m∡ABD = 30° and m∡ABC = 5(30°) = 150°. Note that 30° + 150° = 180°, which is what we expected.

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