Question

Jonas draws two intersecting lines and measures the vertical angles formed. He repeats this for 3 other pairs of intersecting lines. He writes the following conjecture: "The measures of vertical angles are equal." Which of the following statements is true?

a) Vertical angles are not always equal in measure.
b) Vertical angles are always equal in measure.
c) Vertical angles are sometimes equal, depending on the angle.
d) Vertical angles are equal only if the lines are perpendicular.

Answer 1

Jonas's conjecture that 'The measures of vertical angles are equal' is true because vertical angles, which are formed when two lines intersect, always have equal measures.

Step-by-step explanation:

The conjecture made by Jonas, "The measures of vertical angles are equal," is indeed correct. When two lines intersect, they form two pairs of vertical angles.

These angles are opposite each other and are always congruent, meaning they have equal measures. The truth about vertical angles doesn't depend on the lines being perpendicular or on any other characteristic other than the fact that they intersect.

For example, if two lines intersect and form one angle measuring 45 degrees, the vertical angle opposite to it will also measure 45 degrees. Similarly, if the measure of another angle is 110 degrees, its vertical angle will have the same measurement.

This principle is a well-established geometric fact and is true regardless of the specific angle measurements.