As shown in the figure below, points A, B, and D lie on a line. The measure of angle ABC (m∠ABC) is x°, and m∠CBD is (5x+4)°.
Question
Question
As shown in the figure below, points A, B, and D lie on a line. The measure of angle ABC () is x°, and is (5x + 4)°.
Solution
1. Break Down the Problem
We need to determine the relationship between the angles given that points A, B, and D are collinear, with angle ABC measuring and angle CBD measuring . Since these angles are on a straight line, we know that:
2. Relevant Concepts
The angles along a straight line add up to . Therefore, we can set up the following equation based on the information given:
3. Analysis and Detail
Now, we will simplify and solve the equation:
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Combine like terms:
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Subtract 4 from both sides:
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Divide by 6:
4. Verify and Summarize
Now we will verify our result by calculating :
Now, check if the angles add up to :
Final Answer
Thus, the value of is or approximately .
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