This is your perfect answer
It would have an infinite amount of solutions.
Change each equation into y=mx+b form and then do system of equations.
Answer:
m∠3 = 57° → proved down
Step-by-step explanation:
The given is:
- Lines and
- Lines and
- m∠1 = 123°
We want to prove that m∠3 = 57°
∵ // and is the transversal → given
∴ m∠1 = m∠2 → corresponding angles
∵ m∠1 = 123° → given
∴ m∠2 = 123° → equality of two corresponding angles
∵ // and is the transversal → given
∴ m∠2 + m∠3 = 180° → interior supplementary angles
∵ m∠2 = 123° → proved
∴ 123 + m∠3 = 180 → subtract 123 from both sides
∴ m∠3 = 57° → inverse addition property
<span>We can see that line BD and line AC are two parallel lines
which also intersects with other two parallel lines, line BA and line DC. Since
the two sets of parallel lines intersect, then the length of BD = AC and BA =
DC. And by virtue of parallel lines intersecting, then angle BAC and angle BDC
are called corresponding angles. Corresponding angles are angles which have
equal measurement. To summarize the similarities:</span>
<span>BA = DC (Equal
sides)</span>
<span>BD = AC (Equal
sides)</span>
<span>angle BAC = angle BDC (Equal
included angle)</span>
<span>Therefore by using the Side – Angle – Side Postulate, we can
say that triangle ABC and triangle DCB are congruent triangles.</span>
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