Triangle ABC is shown below.
1 answer:
Answer:
C.) 14
Step-by-step explanation:
Look at the triangle: angles b and c have the same arch, so they are congruent.
In a triangle, if two angles are congruent, then the triangle is isosceles, having two equal sides.
The sides opposite the congruent angles are congruent:
∠B → opposite side → AC
∠C → opposite side → AB
The sides AB and AC are equal. Make an equation:
Simplify the equation, solving for x. Add 7 to both sides:
Subtract 2x from both sides:
The value of x is 7. Insert the value of x into the given length of AC:
Simplify multiplication:
Subtract:
Therefore, the length of the line segment AC is 14.
:Done
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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