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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°

User Googlian
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1 Answer

3 votes

Answer:

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

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°.

Find the measures of all angles formed by line a parallel to line b with transversal-example-1
User Esope
by
8.1k points
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