Lines and Angles — Practice Quiz

75°

Step 1: Apply the exterior angle theorem: An exterior angle equals the sum of the two interior opposite angles. Step 2: Let the unknown interior opposite angle be x. Step 3: Set up the equation: 120° = 45° + x. Step 4: Solve for x: x = 120° - 45° = 75°. Step 5: Therefore, the other interior opposite angle is 75°.

20

Step 1: When parallel lines are cut by a transversal, alternate interior angles are equal. Step 2: Set up the equation: 3x + 10 = 5x - 30. Step 3: Rearrange: 10 + 30 = 5x - 3x, so 40 = 2x. Step 4: Solve for x: x = 20. Step 5: Check: 3(20) + 10 = 70° and 5(20) - 30 = 70°, so both angles are equal.

Acute triangle

Step 1: Apply the Triangle Angle Sum Property. The three interior angles of any triangle sum to 180°. Therefore, ∠R = 180° − 40° − 80° = 60°. Step 2: List all three angles: ∠P = 40°, ∠Q = 80°, ∠R = 60°. Step 3: Classify by angle type. An acute triangle has all three angles less than 90°. An obtuse triangle has at least one angle greater than 90°. A right triangle has exactly one angle equal to 90°. Step 4: Since 40° < 90°, 80° < 90°, and 60° < 90°, every angle in triangle PQR is strictly less than 90°. Therefore, triangle PQR is an Acute triangle.

33

Step 1: Interior angles on the same side of a transversal cutting parallel lines are supplementary (sum = 180°). Step 2: Set up the equation: (2x + 20) + (3x - 5) = 180. Step 3: Simplify: 2x + 20 + 3x - 5 = 180, so 5x + 15 = 180. Step 4: Solve: 5x = 165, so x = 33. Step 5: Check: 2(33) + 20 = 86° and 3(33) - 5 = 94°, and 86° + 94° = 180°.