Question

numeric 10 points what is the degree measure of angle 2? (enter the numeric value only)

Explanation:

Step1: Find angle 5

Since an angle and its supplementary angle sum to 180°, for the 125 - degree angle and angle 5, we have $\angle5=180^{\circ}- 125^{\circ}=55^{\circ}$.

Step2: Use the property of parallel lines

Assume the two horizontal lines are parallel. The 40 - degree angle and angle 3 are alternate - interior angles, so $\angle3 = 40^{\circ}$.

Step3: Calculate angle 2

The sum of the interior angles of a triangle is 180°. In the triangle with angles 1, 4, and 5, and considering the relationships of the angles formed by the parallel lines. We know that the sum of angles in the triangle gives us the relationship to find angle 2. Since the 40 - degree angle and angle 3 are equal (alternate - interior angles), and we know angle 5. Angle 2 and the 40 - degree angle and angle 5 are related in the triangle formed. Angle 2 can also be found using the fact that the exterior - angle property of a triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle adjacent to angle 2 is equal to the sum of the 40 - degree angle and angle 5. So $\angle2=40^{\circ}+55^{\circ}=95^{\circ}$.

Answer:

95