Question

If angle 2 equals 9 degrees, state the theorem(s) used to find the values of angle 7 and angle 1.

A) Angle 7 can be found using the Vertical Angles Theorem.
B) Angle 7 can be found using the Corresponding Angles Theorem.
C) Angle 1 can be found using the Alternate Interior Angles Theorem.
D) Angle 1 can be found using the Triangle Angle Sum Theorem.

Answer 1

The correct theorems for finding angles 1 and 7 given angle 2 equals 9 degrees are B) Corresponding Angles Theorem, C) Alternate Interior Angles Theorem, and D) Triangle Angle Sum Theorem, depending on the context of the problem and the position of the angles.

Step-by-step explanation:

The question is about identifying theorems used to find the values of angles given the measurement of one angle. Once we know that angle 2 equals 9 degrees, we can determine the measures of angle 1 and angle 7 by applying particular geometric theorems:

• B) Angle 7 can be found using the Corresponding Angles Theorem if angle 2 and angle 7 are on parallel lines and are in corresponding positions relative to the transversal crossing those lines.
• C) Angle 1 can be found using the Alternate Interior Angles Theorem if angle 1 and angle 2 are on opposite sides of a transversal crossing two parallel lines, making them congruent.
• If angle 1 is part of a triangle, then D) Angle 1 can also be found using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

It is important to note that A) the Vertical Angles Theorem is not applicable here unless it's specifically known that angle 7 is vertically opposite to angle 2.