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Question 8.1.3: Determining Complementary and Supplementary Angles In Fig. 8......

Determining Complementary and Supplementary Angles

In Fig. 8.10, we see that m∡ABC = 31°.

a) ∡ABC and ∡CBD are complementary angles. Determine m∡CBD.

b) ∡ABC and ∡CBE are supplementary angles. Determine m∡CBE.

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a) The sum of two complementary angles must be 90°, so

m∡ABC + m∡CBD = 90°

31° + m∡CBD = 90°

m∡CBD = 90° – 31° = 59°     Subtract 31° from each side of the equation.

b) The sum of two supplementary angles must be 180°, so

m∡ABC + m∡CBE = 180°

31° + m∡CBE = 180°

m∡CBE = 180° – 31° = 149°     Subtract 31° from each side of the equation.

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