Tentukan sama ada garis PQ dan RS adalah selari atau tidak. Nyatakan sebab anda. Determine whether the lines PQ and RS are parallel or not. State your reason.

Question

Asked on August 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-08-14T02:37:56.383Z

Here's how to determine if lines PQ and RS are parallel for each problem: 1) Step 1: Identify the angles. The two angles given are corresponding angles. Angle 1 = 45^ Angle 2 = 45^ Step 2: Check for parallelism. For lines to be parallel, corresponding angles must be equal. Since 45^ = 45^, the corresponding angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their corresponding angles are equal. 2) Step 1: Identify the angles. The two angles given are alternate exterior angles. Angle 1 = 75^ Angle 2 = 75^ Step 2: Check for parallelism. For lines to be parallel, alternate exterior angles must be equal. Since 75^ = 75^, the alternate exterior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate exterior angles are equal. 3) Step 1: Identify the angles. The two angles given are alternate interior angles. Angle 1 = 91^ Angle 2 = 91^ Step 2: Check for parallelism. For lines to be parallel, alternate interior angles must be equal. Since 91^ = 91^, the alternate interior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate interior angles are equal. 4) Step 1: Identify the angles. The two angles given are alternate exterior angles. Angle 1 = 130^ Angle 2 = 130^ Step 2: Check for parallelism. For lines to be parallel, alternate exterior angles must be equal. Since 130^ = 130^, the alternate exterior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate exterior angles are equal. 5) Step 1: Identify the angles. The two angles given are consecutive interior angles (also known as interior angles on the same side of the transversal). Angle 1 = 105^ Angle 2 = 125^ Step 2: Check for parallelism. For lines to be parallel, consecutive interior angles must sum to 180^. Sum = 105^ + 125^ = 230^. Since 230^ ≠ 180^, the sum is not 180^. Step 3: Conclusion. Lines PQ and RS are not parallel because their consecutive interior angles do not sum to 180^. 6) Step 1: Identify the angles. The two angles given are consecutive interior angles. Angle 1 = 63^ Angle 2 = 115^ Step 2: Check for parallelism. For lines to be parallel, consecutive interior angles must sum to 180^. Sum = 63^ + 115^ = 178^. Since 178^ ≠ 180^, the sum is not 180^. Step 3: Conclusion. Lines PQ and RS are not parallel because their consecutive interior angles do not sum to 180^. That's 2 down. 3 left today — send the next one.

Accepted Answer · 2026-08-14T02:37:56.383Z

Here's how to determine if lines PQ and RS are parallel for each problem: 1) Step 1: Identify the angles. The two angles given are corresponding angles. Angle 1 = 45^ Angle 2 = 45^ Step 2: Check for parallelism. For lines to be parallel, corresponding angles must be equal. Since 45^ = 45^, the corresponding angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their corresponding angles are equal. 2) Step 1: Identify the angles. The two angles given are alternate exterior angles. Angle 1 = 75^ Angle 2 = 75^ Step 2: Check for parallelism. For lines to be parallel, alternate exterior angles must be equal. Since 75^ = 75^, the alternate exterior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate exterior angles are equal. 3) Step 1: Identify the angles. The two angles given are alternate interior angles. Angle 1 = 91^ Angle 2 = 91^ Step 2: Check for parallelism. For lines to be parallel, alternate interior angles must be equal. Since 91^ = 91^, the alternate interior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate interior angles are equal. 4) Step 1: Identify the angles. The two angles given are alternate exterior angles. Angle 1 = 130^ Angle 2 = 130^ Step 2: Check for parallelism. For lines to be parallel, alternate exterior angles must be equal. Since 130^ = 130^, the alternate exterior angles are equal. Step 3: Conclusion. Lines PQ and RS are parallel because their alternate exterior angles are equal. 5) Step 1: Identify the angles. The two angles given are consecutive interior angles (also known as interior angles on the same side of the transversal). Angle 1 = 105^ Angle 2 = 125^ Step 2: Check for parallelism. For lines to be parallel, consecutive interior angles must sum to 180^. Sum = 105^ + 125^ = 230^. Since 230^ ≠ 180^, the sum is not 180^. Step 3: Conclusion. Lines PQ and RS are not parallel because their consecutive interior angles do not sum to 180^. 6) Step 1: Identify the angles. The two angles given are consecutive interior angles. Angle 1 = 63^ Angle 2 = 115^ Step 2: Check for parallelism. For lines to be parallel, consecutive interior angles must sum to 180^. Sum = 63^ + 115^ = 178^. Since 178^ ≠ 180^, the sum is not 180^. Step 3: Conclusion. Lines PQ and RS are not parallel because their consecutive interior angles do not sum to 180^. That's 2 down. 3 left today — send the next one.

Tentukan sama ada garis PQ dan RS adalah selari atau tidak. Nyatakan sebab anda. Determine whether the lines PQ and RS are parallel or not. State your reason.

Need help with your own homework?

More Mathematics Questions

Tentukan sama ada garis PQ dan RS adalah selari atau tidak. Nyatakan sebab anda. Determine whether the lines PQ and RS are parallel or not. State your reason.

Need help with your own homework?

More Mathematics Questions