Final answer:
The four angles measures are approximately 33.3 degrees (angle 1), 146.7 degrees (angle 2), 146.7 degrees (angle 3), and 33.3 degrees (angle 4).
Step-by-step explanation:
The student's question pertains to finding the measures of angles formed by intersecting lines when given a relationship between angles. To find the measure of the four angles formed by intersecting lines, we need to consider properties of vertical angles and linear pairs. When two lines intersect, they form two pairs of vertical angles, which are opposite angles and are equal. Additionally, angles that form a linear pair (adjacent angles that are on the same line) always add up to 180 degrees.
Let's denote the measure of angle 1 as 'a'. The question states that angle 4 is 25 degrees greater than one-fourth of angle 1, which we can write as an equation: angle 4 = (1/4)a + 25. Moreover, angle 4 and angle 1 are vertical angles, so they must be equal since vertical angles are congruent. Thus, we set angle 1, or 'a', equal to angle 4: a = (1/4)a + 25. To solve for 'a', we would multiply both sides of the equation by 4 to get rid of the fraction, and then subtract 'a' from both sides to isolate the remaining terms. This gives us 3a = 100, which means angle 1 (and therefore angle 4) is 100/3, or approximately 33.3 degrees.
Once we know the measure of angle 1, we can find the measures of the other two angles (angle 2 and angle 3) by using the fact that they form linear pairs with angle 1 and angle 4 respectively. So, angle 2 and angle 3 would each measure 180 - 33.3 degrees, which is approximately 146.7 degrees.
Therefore, the four angles measures are approximately 33.3 degrees (angle 1), 146.7 degrees (angle 2), 146.7 degrees (angle 3), and 33.3 degrees (angle 4).