In the geometric plane, line is parallel to line . A transversal line intersects line at point and line at point . Ray extends along line to the right of , and ray extends along line to the right of . The measure of interior angle is represented by and the measure of interior angle is represented by . Which of the following statements must be true? Select all such statements.
- The value of is .Answer
- The measure of angle is .Answer
- The acute angle formed by line and line at point measures .Answer
- DThe value of is .
- EAngles and are complementary angles.
Answer
The true statements are that , the measure of angle is , and the acute angle formed by line and line at point measures .
Lines and are parallel, so interior angles on the same side of transversal (angles and ) are supplementary. Solving gives . Substituting yields and . The adjacent angle to at point is , which is acute.
Step-by-Step Solution
Key Concept
Parallel Lines and Consecutive Interior Angles