Answer:
- m∠1=m∠4=m∠5=m∠8=67°;
- m∠2=m∠3=m∠6=m∠7=113°.
Step-by-step explanation:
Consider two parallel lines a and b with transversal m. These lines form 8 angles.
Note that
Since the difference of two angles is 46°, then these angles should be, for example, ∠1 and ∠2. These angles are supplementary, then
m∠1+m∠2=180°.
Solve the system of two equations:
[tex]\left\{\begin{array}{l}m\angle 1+m\angle 2=180^{\circ}\\m\angle 2-m\angle 1=46^{\circ}\end{array}\right.\Rightarrow \left\{\begin{array}{l}2m\angle 2=226^{\circ}\\2m\angle 1=134^{\circ}\end{array}\right.\Rightarrow \left\{\begin{array}{l}m\angle 2=113^{\circ}\\m\angle 1=67^{\circ}\end{array}\right..[/tex]
Then
- m∠1=m∠4=m∠5=m∠8=67°;
- m∠2=m∠3=m∠6=m∠7=113°.
