Question

Find the measures of all angles formed by line a parallel to line b with transversal m, if: e the difference of two angles is 46°

Answer 1

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

• ∠1≅∠4≅∠5≅∠8;
• ∠2≅∠3≅∠6≅∠7.

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:

$\left\{\begin{array}{l}m\angle 1+m\angle 2=180^{\circ}\\m\angle 2-m\angle 1=46^{\circ}\end{array}\right.\Rightarrow \left\{\begin{array}{l}2m\angle 2=226^{\circ}\\2m\angle 1=134^{\circ}\end{array}\right.\Rightarrow \left\{\begin{array}{l}m\angle 2=113^{\circ}\\m\angle 1=67^{\circ}\end{array}\right..$

Then

• m∠1=m∠4=m∠5=m∠8=67°;
• m∠2=m∠3=m∠6=m∠7=113°.