Question

For exercises 11-14., can you make each conclusion from the information in the diagram? Explain

Answer 1

True: 12, 13

False 11, 14

Explanation:

Two lines intersect and form two pairs of vertical angles:

• angles 2 and 4 are vertical;
• angles 3 and the sum of angles 1 and 5 are vertical.

Vertical angles are always congruent, so

`\angle 2\cong \angle 4` (12 statement is true)

`\angle 3\cong \angle 1+\angle 5` (13 statement is true)

Angles 3 and 4 are supplementary angles (add up to 180°), but these angles can have different degree measures, so statement 11 is false.

Statement 14 is false too, because angle 3 can have the degree measure which differs form 90°.