For question 1 the answer is b)
- Congruent angles have the same angle measure, and in a transversal, angles that are opposite around an intersection are congruent. For example ∠ 1 and ∠ 3 are congruent. Because the 2 lines are parallel (and intersected by the same line) the corresponding angles on the other intersection are also congruent. For example if ∠ 1 and ∠ 3 are congruent, then ∠ 5 and ∠ 7 are also congruent.
For question 2 the answer is b) 45°
- ∠ 3 and ∠ 4 are supplementary, meaning they equal 180° together. To solve you just need to subtract, 180° - 135° = 45°
For question 3 the answer is d) 145°
- This combines the previous 2 concepts. ∠ 1 and ∠ 5 are congruent (equal), ∠ 1 and ∠ 2 are supplementary. If ∠ 1 is 180° - 35° = 145°, and ∠ 1 and ∠ 5 are congruent, then ∠ 5 is also 145°.
For question 4 the answer is a) ∠ 1, ∠ 4, ∠ 5, and ∠ 8
- First, ∠ 4 is supplementary because it falls along the same straight line (line m), similarly ∠ 1 is supplementary because it falls along a different straight line (the transversal). Because lines n and m are parallel and both intersected by the transversal, the corresponding angles, ∠ 5 and ∠ 8, are also supplementary.
For question 5, the answer is b) m∠ 3 = 70°
- ∠ 7 is supplementary to the 110° angle, so m∠ 7 = 180°-110° = 70°, ∠ 7 and ∠ 3 are congruent, so m∠ 3 also equals 70°