Lines and Angles

Answer

Step 1: Recall that complementary angles sum to 90° Step 2: Let the complementary angle be x Step 3: Set up equation: 35° + x = 90° Step 4: Solve: x = 90° - 35° = 55° Answer: 55°

Answer

Step 1: Let the angles be 3x and 7x Step 2: Since supplementary angles sum to 180°: 3x + 7x = 180° Step 3: Combine: 10x = 180° Step 4: Solve: x = 18° Step 5: Find angles: 3x = 3(18°) = 54°, 7x = 7(18°

Answer

Step 1: Vertically opposite angles are equal Step 2: Given angle = 65° Step 3: Vertically opposite angle = 65° Step 4: Adjacent angles are supplementary (sum = 180°) Step 5: Other two angles = 180° -

Answer

Step 1: Recall corresponding angles axiom Step 2: When parallel lines are cut by a transversal, corresponding angles are equal Step 3: Given angle = 110° Step 4: Corresponding angle = 110° Answer: 110

Answer

Step 1: Alternate interior angles are equal when lines are parallel Step 2: Set up equation: 3x + 15 = 2x + 40 Step 3: Subtract 2x from both sides: x + 15 = 40 Step 4: Subtract 15 from both sides: x =

Answer

Step 1: Use angle sum property: ∠A + ∠B + ∠C = 180° Step 2: Substitute known values: 60° + 45° + ∠C = 180° Step 3: Simplify: 105° + ∠C = 180° Step 4: Solve for ∠C: ∠C = 180° - 105° = 75° Step 5: Verif

Answer

Step 1: Let angles be 2x, 3x, and 4x Step 2: Use angle sum property: 2x + 3x + 4x = 180° Step 3: Combine: 9x = 180° Step 4: Solve: x = 20° Step 5: Find angles: 2x = 40°, 3x = 60°, 4x = 80° Step 6: Ver

Answer

Step 1: Use exterior angle theorem Step 2: Exterior angle = Sum of two interior opposite angles Step 3: Exterior angle = 35° + 48° Step 4: Exterior angle = 83° Step 5: Verify: Third interior angle = 1