Question

Given: angle1 and angle2 are supplements, angle3 and angle4 are supplements, and Angle 1 ᵃngle4. Prove: angle 2 ^ Angle 3

Options:
A) angle 2 ᵃngle 3
B) angle 1 ᵃngle 4
C) angle 1 ᵃngle 3
D) angle 2 ᵃngle 4

Answer 1

To prove which angles are congruent, we used the fact that supplementary angles add up to 180 degrees and that angle1 is congruent to angle4. By substitution and comparison, we deduced that angle2 is congruent to angle3. The correct answer is A) angle2 is congruent to angle3.

Step-by-step explanation:

The student is asked to prove which angles are congruent given that angle1 and angle2 are supplements, angle3 and angle4 are supplements, and angle1 is congruent to angle4. To solve this, we will use the property that supplementary angles add up to 180 degrees.

If angle1 and angle2 are supplements, then:

angle1 + angle2 = 180 degrees

As angle1 is congruent to angle4, we can replace angle1 with angle4:

angle4 + angle2 = 180 degrees

Similarly, if angle3 and angle4 are supplements, then:

angle3 + angle4 = 180 degrees

As both equations equal 180 degrees, and angle4 is common to both, we can deduce that angle2 must be congruent to angle3:

angle2 = angle3

Therefore, the correct answer is A) angle2 is congruent to angle3.