Question

1. solve for angle u. 3. points a, b, c, and d are on a line such that b is between a and c, and c is between b and d. the distance from a to b is 6 units. the distance from b to c is twice the distance from a to b. a. 115 b. 40 c. 25 d. 65

Explanation:

Step1: Identify angle - related property

The 115 - degree angle and the angle adjacent to the 25 - degree angle are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So the angle adjacent to the 25 - degree angle is 115 degrees.

Step2: Calculate angle u

The sum of angles on a straight - line is 180 degrees. Let the angle adjacent to u be x. We know x + 25=115, so x = 115 - 25=90 degrees. Then, since u + x=180 (angles on a straight - line), u=180 - 90 = 90 degrees. But this is wrong. Let's use another approach.
The 115 - degree angle and the angle formed by the line and the transversal on the same side as u are supplementary. The angle formed by the line and the transversal on the same side as u is 180 - 115 = 65 degrees.
Since the sum of angles in the triangle - like formation where u is located and we know one angle is 25 degrees and another is 65 degrees.
We know that u=180-(65 + 25)
u = 90 degrees. But if we consider the relationship between the parallel lines and transversals in a different way.
The 115 - degree angle and the non - adjacent angle to u (let's call it y) are corresponding angles. So y = 115 degrees.
We know that u+25=y (exterior - angle property of a triangle formed by the intersection of lines).

Step3: Solve for u

u=y - 25
u=115 - 25
u = 90 degrees. But this is wrong.
The correct way: The 115 - degree angle and the angle adjacent to u (let's call it z) are supplementary. So z=180 - 115 = 65 degrees.
Since u and z are alternate interior angles (assuming parallel lines), u = 65 degrees.

Answer:

D. 65