Pre-Calculus Homework Solutions 66

Pre-Calculus Homework Solutions 66 - 8. m ADE 9x 5...

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8. Explore: From the figure, you know that m / ABC 5 5 x 1 90 and m / ADE 5 14 x 1 9. You also know that / ABC and / ADE are corresponding angles. Plan: For line , to be parallel to line m ,the corresponding angles must be congruent. So, m / ABC 5 m / ADE . Substitute the given angle measures into this equation and solve for x . Solve: m / ABC 5 ¬ m / ADE 5 x 1 90 5 ¬ 14 x 1 9 90 5 ¬ 9 x 1 9 81 5 ¬ 9 x 9 5 ¬ x Examine: Now use the value of x to find m / ABC . m / ABC 5 ¬ 5 x 1 90 5 ¬ 5(9) 1 90 5 135 Verify the angle measure by using the value of x to find m / ADE .That is, 14 x 1 9 5 14(9) 1 9 or 135. Since m / ABC 5 m / ADE , / ABC > / ADE and , i m . 9. Explore: From the figure, you know that m / ABC 5 7 x 1 3 and m / ADE 5 9 x 2 5. You also know that / ABC and / CBD are supplementary, and / CBD and / ADE are alternate interior angles. Plan: For line , to be parallel to line m ,the alternate interior angles must be congruent. So, m / CBD 5 m / ADE ,where m / CBD 1 m / ABC 5
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