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Question 8.1.4: Determining Complementary Angles If ∡ABC and ∡CBD are comple......

Determining Complementary Angles

If ∡ABC and ∡CBD are complementary angles and m∡ABC is 26° less than m∡CBD, determine the measure of each angle (Fig. 8.11).

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Let m∡CBD = x. Then m∡ABC = x – 26, since it is 26° less than m∡CBD. Because these angles are complementary, we have

m∡CBD + m∡ABC = 90°

x + (x – 26°) = 90°

2x – 26° = 90°

2x = 116°

x = 58°

Therefore, m∡CBD = 58° and m∡ABC = 58° – 26°, or 32°. Note that 58° + 32° = 90°, which is what we expected.

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