Answer:
1. m ∠ 1 = 113°
2. m ∠ 2 = 67°
3. m ∠ 4 = 67°,
4. m ∠ 5 = 113°
5. m ∠ 6 = 67°
6. m ∠ 7 = 113°
7. m ∠ 8 = 67°
Step-by-step explanation:
Given AB║CD and m║n and m∠3=113°
Solution, since m and n are parallel lines so AB and CD are transversal lines.
So ∠2 and ∠3 makes a linear pair whose sum is equal to 180°.
(∠2 and ∠8),(∠3 and ∠7),(∠1 and ∠5),(∠4 and ∠6) are alternate interior angles.
(∠2 and ∠4),(∠1 and ∠3),(∠5 and ∠7),(∠6 and ∠8) are corresponding angles.
When two lines are parallel and their is a transversal line then the measure of alternate angles are equal and also the measure of corresponding angles are equal.
[tex]m\angle 2 + m\angle 3 = 180\\m\angle 2 + 113 = 180\\m\angle2=180-113=67\\m\angle2=m\angle8=67 \ (alternate\ interior\ angle)\\m\angle3=m\angle7=113 \ (alternate\ interior\ angle)\\m\angle3=m\angle1=113 \ (corresponding\ angle)\\m\angle2=m\angle4=67 \ (corresponding\ angle)\\m\angle4=m\angle6=67 \ (alternate\ interior\ angle)\\m\angle1=m\angle5=113 \ (alternate\ interior\ angle)[/tex]
Hence the measure of all angles are:
1. m ∠ 1 = 113°
2. m ∠ 2 = 67°
3. m ∠ 4 = 67°,
4. m ∠ 5 = 113°
5. m ∠ 6 = 67°
6. m ∠ 7 = 113°
7. m ∠ 8 = 67°
