What is the solution with steps---8th GRADE MATH WORK
TEST 89 - Angle
1. Lines d₁ and d₂ are parallel. What is the value of the 2x?
A) 20
B) 11
C) 12
D) 13
**Chart/Diagram Description:**
* **Type:** Geometric diagram showing two parallel lines intersected by a transversal line.
* **Main Elements:**
* Two horizontal lines labeled d₁ (top) and d₂ (bottom). Arrows on the right indicate the lines extend indefinitely. The problem statement says d₁ and d₂ are parallel.
* A transversal line intersects both d₁ and d₂ from top left to bottom right.
* An angle is labeled 45° in the upper region, between the transversal and the line d₁, on the right side of the transversal. This angle is an acute angle.
* An angle is labeled 4x+5° in the lower region, between the transversal and the line d₂, on the left side of the transversal. This angle is an acute angle.
*(Note: There is also a partial image of another problem on the left side, showing lines d1 and d2 and an angle of 25 degrees, but the question stem and options are not fully visible. There are also fragments of questions 6 and 7 visible on the right, but the content is incomplete).*
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Let's solve this step by step. We have two parallel lines d₁ and d₂ intersected by a transversal. We can see a 45-degree angle and an angle labeled 4x plus 5 degrees. These are alternate interior angles, which means they are equal when lines are parallel.
Since the lines are parallel, the 45-degree angle and the 4x plus 5 degree angle are alternate interior angles. By the alternate interior angles theorem, these angles must be equal. So we can set up the equation: 45 equals 4x plus 5.
Now let's solve the equation step by step. We start with 45 equals 4x plus 5. First, we subtract 5 from both sides to get 40 equals 4x. Then we divide both sides by 4 to find that x equals 10.
Now we need to find the value of 2x. Since we found that x equals 10, we can calculate 2x by multiplying 2 times 10, which gives us 20. Looking at our answer choices, this matches option A. Therefore, the answer is A, 20.
Let's review our complete solution. We identified that the 45-degree angle and the 4x plus 5 degree angle are alternate interior angles. We set up the equation 45 equals 4x plus 5, solved to find x equals 10, then calculated 2x equals 20. Therefore, the correct answer is A, 20.