In the trapezoid below, if m∠𝐵𝐴𝐶∠𝐵𝐴𝐶 = (3x - 4)° and m∠𝐷𝐶𝐴∠𝐷𝐶𝐴 is (2x + 9)°, find x.
Question
In the trapezoid below, if m∠𝐵𝐴𝐶∠𝐵𝐴𝐶 = (3x - 4)° and m∠𝐷𝐶𝐴∠𝐷𝐶𝐴 is (2x + 9)°, find x.
Solution
In a trapezoid, the sum of two adjacent angles is 180 degrees. Therefore, we can set up the following equation:
(3x - 4) + (2x + 9) = 180
Combine like terms:
5x + 5 = 180
Subtract 5 from both sides:
5x = 175
Finally, divide both sides by 5 to solve for x:
x = 35
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